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1
Mix flour, salt, and yeast together in a bowl. Add water and olive oil and stir until the mixture forms a rough ball. Dump dough onto a lightly floured surface and knead into a neater ball for a minute or two. Lightly coat the bowl with olive oil. Return dough to the bowl and roll around to coat in oil. Cover the bowl and let sit until doubled in size, about 2 hours.
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2
Dump the dough onto a floured surface and press air out using the palm of your hand. Fold dough back into a ball, cover, and let sit 20 minutes more.
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3
Preheat the oven to 500 degrees F (260 degrees C). Sprinkle a pizza stone or baking sheet with cornmeal.
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4
Roll and stretch dough into a thin circle roughly 12 inches in diameter. Place dough on the prepared baking stone.
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5
Hold an asparagus stalk by the thick end and lay it flat on a cutting board. Use a vegetable peeler to create long shavings into a bowl. Repeat with remaining stalks and discard tough ends. Add 2 teaspoons olive oil and salt and toss to coat.
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6
Sprinkle Parmesan cheese on top of the dough followed by mozzarella cheese. Add shaved asparagus.
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7
Bake in the preheated oven until crust is browned and bubbly and asparagus is lightly charred, 10 to 15 minutes.
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8
Top with green onions before slicing and serving.
