Heat the oil in a large skillet over medium-high heat. Add the Mexican chorizo and cook, breaking it up with a spoon, until it's fully browned and cooked through, about 7-10 minutes.
Add the chopped onion and bell pepper to the skillet with the chorizo. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes. Drain off any excess grease.
Set the oven temperature to 350 degrees.
Carefully slice each croissant horizontally, almost all the way through, creating a pocket for the filling.
Evenly divide the chorizo and vegetable mixture among the four croissants, stuffing it into the sliced openings.
Sprinkle the shredded cheese generously over the chorizo filling in each croissant.
Place the filled croissants on a baking sheet. Bake for 8-12 minutes, or until the cheese is melted, bubbly, and lightly browned, and the croissants are heated through.
Remove the croissants from the oven and let them cool slightly before serving. Garnish with optional toppings if desired.