Preheat oven to 425°F.
Combine 1 cup flour, undissolved yeast, sugar and salt in a large bowl. Add very warm water and oil; mix until well blended, about 1 minute.
Gradually add enough remaining flour to make a soft dough. Dough should form a ball and will be slightly sticky. Knead on a floured surface, adding additional flour if necessary, until smooth and elastic, about 4 minutes. (If using RapidRise Yeast, let dough rest at this point for 10 minutes.) Cover and let rest.
Cook chorizo in large nonstick skillet over medium-high heat; drain grease.
Pat dough with floured hands to fill greased pizza pan or baking sheet. OR roll dough on a floured counter to 12-inch circle; place in greased 12-inch pizza pan or baking sheet. Form a rim by pinching the edge of the dough.
Top crust with cheese, chorizo and green onions. Form 5 "wells" by pushing aside toppings; 4 near the outer edge, 1 in the middle. Crack each egg and place into a well.
Bake on lowest oven rack for 12 to 15 minutes, until cheese is bubbly and crust is browned. IF egg is not cooked to desired doneness after 15 minutes, move rack to highest position in oven. Broil 1 to 2 minutes for desired egg doneness.
*If you don't have a thermometer, water should feel very warm to the touch.