Pour the oil onto a sheet pan and then arrange the tortillas on it, spreading them around on both sides so they are coated in the oil. Bake on a middle rack for 15-17 minutes or until the tortillas are crisp. Remove from the oven.
Arrange an oven rack 6 inches from the heating element. Turn on the broiler.
After a few minutes, when cool enough to handle, arrange the tortillas evenly spaced across the sheet pan if they’re not already.
On each crisped tortilla, place in the center 1 or 2 pickled jalapeño slices. Next, sprinkle 1 tablespoon of shredded Monterey Jack cheese evenly over the tortilla and jalapeño. Lastly, place a yellow Cheddar square in the center over the pepper.
When all are topped, place the pan under the broiler and cook until the cheese has melted, 1-2 minutes. Serve immediately with salsa.