Jesse Cool, a restaurateur and cookbook author, keeps a garden in Palo Alto, Calif., on the grounds of Standford University that is so large she jokingly refers to it as “the farm of Silicon Valley.” There is a chicken coop, a greenhouse, twelve vegetable and fruit beds, and two compost piles. It is picturesque and fertile, a perfect example of California’s legendary bounty, and a striking contrast to the plot that her father kept behind his grocery store in Greensburg, Pa., a small coal mining town. It was just big enough to keep his family in tomatoes and peppers, with a few watermelon and cucumber plants between the shrubberies.

“As a kid I was so embarrassed that my father gardened,” Cool says, “but as an adult, I am extremely proud of his respect for growing food close by.”

Working in her father’s garden, Cool learned his philosophy of organic, earth-to-table eating. The food she raises feeds her family — her husband, eldest son, daughter-in-law, two grandchildren, as well as her youngest son, visiting on breaks from postgraduate work at Duke. Friends and customers of her three restaurants — Flea Street Café, jZCool Eatery and Wine Bar, and the Cool Café at the Stanford University Cantor Arts Center — are also beneficiaries of her garden’s bounty.

Cool finds that getting her two grandchildren involved in every stage of food production and consumption gives her the opportunity to spend time with them while also teaching them ways to make healthy choices.

Masa, 8 years old, and Miya, 3, plant seedlings, gather eggs, and pull carrots out of the dirt. Recently, Masa announced that he has even started to save the trimmings from his cooking experiments at home for two compost piles in their backyard: one “with worms” and one “without.”

“Nothing could make me prouder,” Cool says.

Nothing, that is, except that her grandson also has an adventurous palate and an appreciation for fine dining. Once a month or so, Cool takes Masa on “dates.” They dress up and go to some of the best restaurants in the region, including Fish in Sausalito, where Masa, at the age of 6, ate a half-dozen barbecued oysters and a bowl of clam chowder. A boy ordering a spinach salad or sushi à la carte gets some raised eyebrows from restaurant staff and other diners, but Ms. Cool laughs it off. She sees their dates as opportunities to share with him the pleasures of the table. The eatery may be high end, but Cool doesn’t stand on ceremony when it comes to giving Masa the best dining experience.

“I’m anything but stuffy,” she says. If her young companion get antsy waiting for the main course to arrive, they pull out word puzzles and mazes to keep occupied.

Another of Cool’s favorite activities to do with her grandchildren — one that she did with her two sons when they were young — is to bring them to a farmers’ market or grocery store and give them $5 to spend.

“The only rule is, no breads, no snacks, no sweets, nothing out of a box,” she says. They’re challenged to try new, whole foods, and they begin to make buying decisions that, Cool hopes, will influence the way they cook and eat for the rest of their lives.

“It’s so interesting what they come back with, like radishes, asparagus, and heirloom baby carrots and organic — always organic — strawberries. It’s fun to either eat the produce right away or find some way to cook it, together.”

In springtime, Masa and Miya’s riotous mix of young vegetables, picked up at the market or dug out of their grandma’s garden, pair beautifully with stewing meat from grass fed animals — meat that Cool purchases from sellers she knows by name. Or she might make pan-fried cakes of sugar snap peas, potato, and Cheddar.

“Sugar snap peas and potato, you can’t get much more kid-friendly than that,” she says.

But perhaps Cool’s favorite kitchen activity is making gnocchi with her grandchildren. When the green onions really start coming in, she uses them to flavor ricotta-based gnocchi, which she shows Masa and Miya how to form into little footballs, just as she once taught her sons.

“My sons could not understand why gnocchi, chicken soup, and pie crust were mandatory lessons in the kitchen,” Cool says, “but as adults, they now realize all three dishes are extremely adaptable to any season and can win the way into anyone’s heart.”

Continue to the recipes: Oven Roasted Beef Stew With Baby Spring Vegetables, Ricotta & Green Onion Gnocchi, and Sugar Snap Pea, Potato, & Cheddar Cakes