Meanwhile, in a medium skillet, heat the oil over medium heat. Add the chorizo, stirring occasionally and breaking up with a spatula, until the chorizo is browned, about 10 minutes.
Remove from skillet with a slotted spoon to a paper towel lined plate to drain the grease off, but leave the drippings in the skillet.
With the heat still on medium, whisk in the flour and cook, whisking constantly, until roux is very smooth and starting to turn a light golden brown, about 5 minutes. Gradually stir in the milk, whisking constantly until incorporated. Reduce heat to medium-low and cook gravy, whisking constantly, until thickened, 5–8 minutes. Stir chorizo into gravy; season with salt, pepper, and hot sauce.
When waffles and gravy are both done, plate waffles and spoon gravy over the top. Top with shredded cheddar, sour cream, and chopped green onions, if desired.