In the bowl of a stand mixer fitted with a dough hook, stir together Water (1 cup), Active Dry Yeast (1 1/2 teaspoon), and Honey (1/2 teaspoon). Allow to ferment for 6-8 minutes.
Stir in most of the All-Purpose Flour (2 cup), as well as Olive Oil (2 tablespoon), Dried Basil (1/2 tablespoon), and Kosher Salt (1 teaspoon). Begin kneading, allowing all the flour to be absorbed before adding more.
Add additional flour gradually until dough is soft and no longer sticky to the touch, about 8 minutes. The exact amount of flour will vary.
Lightly coat a large bowl with additional olive oil. Shape dough into a ball and place in bowl. Cover and allow to rise in a warm, draft-free area until double in size, about 1 hour.
Slice Prosciutto (8 slice) into 1/4-inch strips. Heat a non-stick skillet over medium-high and cook prosciutto until crisp, stirring often. This will take 8-10 minutes. Remove to a paper towel-lined plate.
Preheat a grill to medium heat.
Cut the woody 1 to 2 inches off the bottom of the Asparagus (12 piece). If they are thick spears, shave the sides lightly with a vegetable peeler to make them uniform in width. Rub spears lightly with olive oil and season with Salt and Pepper (to taste).
Place asparagus directly on grill against the grain of the grills. Grill for 4-6 minutes until crisp-tender, turning once or twice. Remove from grill and set aside.
In a small bowl, whisk together Olive Oil (3 teaspoon), Lemon Juice (1 tablespoon), Dried Basil (1/2 teaspoon), Salt (1/4 teaspoon), and a few grinds of black pepper. Cut asparagus into 1-inch pieces and toss with the dressing, saving the remainder for finished flatbread.
Deflate the dough by kneading 3 to 4 times and divide the dough into two portions. Cover lightly and allow the dough to rest for 10 minutes. This will help relax the dough and make it easier to flatten.
Spread and press one portion out to an approximate 13x8-inch rectangle on a flat, movable surface like a cutting board or back of a baking tray.
Peel dough off of surface in one motion if possible and lay on preheated grill. Spread out corners slightly if possible. Close lid and cook for about 5-6 minutes until golden and crisp on the bottom. The time will vary depending on your grill and heat setting.
Poke any large air bubbles and flip dough over.
Immediately scatter on half of the asparagus, prosciutto, and Goat Cheese (3 ounce). Sprinkle with Grated Grated Parmesan Cheese (1/4 cup) and close the lid. Allow to cook for 3-4 more minutes to warm toppings and finish cooking the dough.
Remove to a cutting board and cut into wedges. Drizzle with remaining dressing, top with Grated Parmesan Cheese (1/4 cup) and serve immediately.