Place jalapeño havarti and apple slices on tortilla. Top with the other tortilla.
Heat oil in a pan. Add quesadilla, and cook until golden brown. Flip and cook the other side. Slice and serve.
If you can't find vegan jalapeño havarti, you can use 4 tablespoons finely chopped jalapeño, 4 tablespoons vegan cream cheese (optional, but it adds the rich, creaminess that the havarti has) and 10 slices vegan Monterey Jack.