Preheat oven to 400 degrees.
Roll the dough into a roughly 10” x 14” square. Pierce the dough with a fork randomly. Brush dough lightly with 1 Tblsp. olive oil and sprinkle the dill all over. Bake the dough for 10 minutes, until puffy and just lightly browned. Remove the partially-baked dough from the oven.
While the dough is baking, quickly blanch the asparagus for two minutes and remove to an ice bath to stop the cooking process. Drain on paper towels.
Leave oven on. Place a layer of the mixed cheeses all over the bread base and add the asparagus, half going one way and half going the other way. Finish by topping the asparagus with the rest of the cheese. Add salt and pepper to taste, and drizzle with olive oil.
Bake at 400 degrees another 10-14 minutes, or until cheese is bubbly around asparagus. Remove from heat and cool completely.
Slice into pieces so that each piece has an asparagus spear. Serve at room temperature.
Make ahead of time:
This appetizer can be made ahead of time and stored in the refrigerator in an airtight plastic container.
Makes about 20 appetizers.