Heat the oven to 425°F and grease a 9-by-13-inch baking dish.
Toss the sweet potatoes with the olive oil, salt and pepper in the dish and roast for 20 minutes, stirring once.
Brown the chorizo and bell pepper in a skillet over medium-high heat for 7 to 9 minutes, breaking up the meat, until the chorizo reaches 160°F.
Scatter the chorizo mixture and 1 cup pepper Jack over the roasted sweet potatoes.
Whisk the eggs and milk until smooth and pour them evenly into the dish.
Lower the oven to 375°F, add the remaining cheese and bake for 22 to 27 minutes, until the center reaches 160°F and no liquid egg remains.
Rest for 10 minutes before slicing.