Heat a large skillet over medium. Add pancetta and cook, stirring occasionally, until the pancetta is crispy and it renders fat, about 6 minutes. Remove pancetta from skillet (reserve fat). Set skillet aside.
Meanwhile, place bread in the bowl of a food processor. Process until coarse crumbs form (you should have about 2 cups). Slice the stem end off the tomatoes and use a spoon or melon baller to remove the contents (leaving outer flesh intact to form a cup). Season inside of tomatoes with salt and pepper.
Return skillet to medium heat and add thyme leaves to fat in pan. Add breadcrumbs and walnuts to skillet and cook, stirring occasionally, until golden brown, 5 minutes. Transfer breadcrumbs to a large bowl; wipe out skillet.
Return skillet to high heat and add olive oil. Add Swiss chard to skillet and cook, tossing occasionally, until wilted, tender, and liquid has evaporated, 2 to 3 minutes. Stir in red-wine vinegar and season with salt and pepper. Stir together cooked chard and breadcrumb mixture. Spoon filling into prepared tomatoes and sprinkle with pancetta. Place tomatoes on a serving platter and drizzle with remaining olive oil and vinegar.
Before her diagnosis, Caroline wrote a book on cakes called Cake Magic!. She started developing a birthday cake using her gluten-free mix found in that book. Check out other recipes she’s developing for her new life—and the stories behind them—on her blog, The Wright Recipes. Her next book, Soup Club, is a collection of recipes she made for her underground soup club of vegan and grain-free soups she delivers every week to friends throughout Seattle's rainy winter. (Available February 2021.)