Heat olive oil in a medium-sized saucepan. Add onion and garlic, saute for approximately 5 minutes or until starting to soften. Sprinkle flour over onion mixture, stir and cook for two minutes. Stir in evaporated milk and continue to cook until thickened and heated through, about 3-5 minutes. Add a large pinch of salt (a pinch is three fingers and a thumb) and freshly ground black pepper.

Add cheese and stir until incorporated (mixture will be very thick). Add half & half a few tablespoons at a time, stirring to incorporate, until you reach desired consistency. Stir in minced hatch chiles and stir until very hot. Serve immediately with bread cubes or tortilla chips.