In the bowl of a stand mixer fitted with the paddle attachment, beat 2 cups (250g) flour, Platinum Instant Sourdough Yeast, and kosher salt at low speed until well combined.
In a small saucepan, heat water, milk, 2 tablespoons (30g) oil, and honey over medium heat until an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add milk mixture to flour mixture; beat at medium speed for 2 minutes. Reduce mixer speed to low; gradually beat in 1 1/2 cups (188g) flour until a very soft, sticky dough is formed.
Switch to the dough hook attachment. Beat at medium-low speed for 13 minutes. (Dough should almost pull away from sides of bowl.) Add up to remaining 1/4 cup (31g) flour, 1 tablespoon (8g) at a time, if necessary. (Avoid adding too much flour; a slack dough is important for a light, airy crust.) (Dough should pass the windowpane test; see Note.) Using well-floured hands, shape dough into a ball.
Lightly oil a large bowl. Place dough in bowl, turning to grease top. Cover with plastic wrap, and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, about 1½ hours.
Punch down dough. Divide dough in half (about 390g each). Using floured hands, shape each half into a smooth ball, and place each in a lightly oiled small bowl. Lightly brush tops with oil. Cover with a double layer of plastic wrap, and refrigerate overnight*.
About 1½ hours before baking, remove dough from refrigerator. Place a pizza stone on lowest oven rack. Preheat oven to 475°F (250°C). (Allow at least 1 hour for pizza stone to fully heat before baking.)
In a small microwave-safe bowl, combine garlic, lemon zest, and remaining 1 1/2 tablespoons (21g) oil. Heat on high until mixture begins to bubble, about 20 seconds.
Generously dust a pizza peel or a rimless baking sheet with flour and cornmeal.
For each flatbread, drape each portion of dough over your knuckles. Using both hands, gently stretch dough with knuckles to form a 3/8-inch-thick oval, being careful not to press out any air bubbles. Place dough on prepared pizza peel, stretching to even out any thick areas. Shake pizza peel a few times to make sure dough always stays loose, dusting bottom with additional cornmeal if needed. (Continue to check dough a few times while topping. Dough must remain loose to slide easily onto pizza stone.)
Evenly spoon half of garlic mixture onto each flatbread. Top each with half of fontina and half of Parmesan; top each with half of zucchini, half of squash, and half of onion. Slide 1 flatbread onto hot pizza stone.
Bake until crust is deep golden brown, 10 to 12 minutes, using tongs to rotate flatbread halfway through baking. Immediately garnish with fontina, sea salt, basil, and parsley, if desired.
Repeat procedure with remaining flatbread. Immediately garnish with fontina, sea salt, basil, and parsley, if desired.