Combine the parsley, basil, chives, grated Parmesan, minced garlic, lemon zest, and lemon juice in a food processor and blend until you have a coarse paste. Slowly drizzle in the 1/3 cup olive oil while pulsing until the pesto reaches a spreadable consistency—you want some texture, not a completely smooth puree. Stir in the red pepper flakes and set aside. I find that making the pesto while the grill heats means it has time to marry the flavors.
While the pesto sets, prepare your vegetables: cut the zucchini into 1/2-inch thick planks, trim the tough woody ends from the asparagus, slice the red onion into 1/2-inch rings (keep the rings intact with toothpicks if they fall apart), and prepare the corn ears by removing the husks and silk. Place all vegetables in a large bowl, drizzle with the 1/4 cup olive oil, and season generously with the salt and cracked black pepper. Toss gently to coat everything evenly.
Preheat your grill to 375°F. Once it reaches temperature, begin grilling the vegetables in batches, starting with the corn and asparagus (which cook fastest at about 5-8 minutes), followed by the zucchini and onion rings (10-15 minutes each). Work in batches so you don't overcrowd the grill, and arrange vegetables in a single layer. You're looking for light char marks and tender flesh—the vegetables should have some give when pierced with a fork. As each batch finishes, move it to a clean plate and keep it warm.
Brush both sides of each flatbread lightly with the vegetable oil—this prevents sticking and creates a nice crust. Place them directly on the grill and cook for 1-2 minutes per side until you see light char marks and the bread is warm and slightly crispy. I like to keep the flatbreads on the edge of the grill while the vegetables finish cooking so they stay warm without drying out.
While the flatbreads are warm, cut the corn kernels from the cob by standing each ear upright and running a sharp knife down the sides. Spread a generous layer of the herb pesto from Step 1 onto each warm flatbread, leaving a small border. Arrange the grilled vegetables on top in any pattern you like—distribute the corn kernels, zucchini planks, asparagus spears, and onion rings across each flatbread. Top each one with a dollop of ricotta, letting it fall naturally across the vegetables for a rustic presentation.
Slice each flatbread into thirds or quarters, depending on your preference, and transfer to a serving platter. Serve immediately while everything is still warm, with fresh lemon wedges on the side for guests to squeeze over their portions for a bright finish.