How to Make It
Preheat oven between to 475° and 550°F with rack in the lower third. Place a pizza stone or baking sheet on the rack.
On a lightly floured surface, roll (or push and pull) dough to a 16-inch oval, about 12 inches wide, or as close to a circle as you can make it. If the dough springs back, let it rest 5 minutes and try again. Transfer to a piece of parchment paper, drizzle with oil, and season with salt and pepper. Set aside.
Heat oil in a large nonstick skillet over medium-high heat. Remove sausage from casing and add to skillet. Cook, breaking up with a wooden spoon, until browned and nearly cooked through, about 4 minutes. Transfer to a plate using a slotted spoon.
Add potatoes to skillet, season with salt and pepper, and cook, turning occasionally, until golden and tender, about 5 minutes. Transfer to plate with sausage.
Reduce heat to medium-low. Season eggs with salt and pepper and add to skillet, stirring vigorously until about half of the eggs are set. Remove from heat and immediately transfer to prepared dough, spreading almost to the edge. Top with half of the cheddar, potatoes, sausage, then remaining cheddar.
Carefully remove hot stone or baking sheet from the oven and place pizza and parchment on top. Return to oven and bake until dough is golden and risen, and cheese is melted and bubbly (be sure to peek underneath to check that the bottom of the pizza is golden, too). Top pizza with jalapeño or hot sauce if using.