Combine the asparagus, basil, garlic and pine nuts in a food processor and pulse a few times to coarsely chop. With the motor running, slowly add the oil and process until emulsified. Season with salt and pepper and transfer the pesto to a bowl. Stir in the Pecorino Romano.
Place pizza shell on the grill. Grill until slightly crisp, about 1 minute. Remove the shells and spread each with the pesto. Top with the fontina, return to the grill, close the cover and continue cooking until the cheese has melted, 2 to 3 minutes. Remove from the grill and sprinkle with the remaining Romano cheese and chopped fresh basil. Slice each flatbread into bite-sized pieces.