Preheat the griddle to 300° F. Cook the 4 pizza rounds for 30 seconds on each side. Remove from the heat and set aside.
Preheat the oven to 500° F. Wash the asparagus and place on a lightly oiled baking sheet. Roast the asparagus in the hot oven until charred, about 9 minutes. Remove from the oven. When the asparagus are cool enough to touch, cut each stalk into 3 pieces.
In a small bowl, mix the goat cheese and olive oil. Divide the goat cheese mixture between the 4 pizzas, making sure to leave a 3/4-inch rim around the pizza for the crust. Smooth the goat cheese so that the topping is only 1/8- to 1/4-inch thick. Scatter the asparagus over the pizzas and cook the pizzas on the griddle until the dough is done, but not brown, about 3 1/2 minutes. Serve immediately.