Step 1

Pulse flour, 1 teaspoon salt, and sugar in a food processor until combined. Add butter and shortening; pulse until mixture resembles coarse meal, with some pea-size pieces remaining. Stir vinegar into ice water; drizzle 3 tablespoons over flour mixture and pulse several times to combine. Add more ice water, 1 tablespoon at a time, and pulse until mixture holds together when pinched. Shape dough into a rectangle and wrap in plastic. Refrigerate until firm, at least 1 hour and up to 1 day (or freeze up to 3 months; thaw overnight in refrigerator before using).

Step 2

Brush a 9-by-13-inch rimmed baking sheet or baking pan with shortening; line with parchment, leaving a 1-inch overhang on long sides. Transfer dough to a lightly floured work surface and roll out to a 12-by-15-inch rectangle. Transfer to prepared sheet, fitting dough into corners and tucking overhanging dough under. Refrigerate until chilled, about 20 minutes.

Step 3

Meanwhile, bring a large pot of salted water to a boil. Slice cauliflower lengthwise through core to make 1/2-inch-thick steaks. Slice broccoli lengthwise through stems into 1/2-inch-thick pieces (it's okay if they come apart slightly). Blanch cauliflower until just tender, 4 to 5 minutes. Remove with a slotted spoon and transfer to a plate. Blanch broccoli until bright green and crisp-tender, 2 to 3 minutes; transfer to a separate plate. Blanch carrots until crisp-tender, about 3 minutes; transfer to a separate plate. Drizzle each plate of vegetables with 1 teaspoon oil. Toss zucchini in a bowl with thyme and remaining 1 teaspoon oil; season with salt and pepper.

Step 4

Preheat oven to 425°F. Sprinkle panko evenly over bottom of dough, then sprinkle with fontina. Top with an even layer of cauliflower, then broccoli. Top with half of cheddar, then carrots, then zucchini. Sprinkle with remaining cheddar.

Step 5

Arrange tomato slices on top; season with salt and pepper and drizzle with oil. Bake until crust is golden brown and filling is bubbling around edges, 45 to 50 minutes. Let cool slightly. To serve, lift from pan using parchment overhang, then slice.