In a large bowl, whisk together the salsa, garlic, lime juice, chile powder and 1/4 cup vegetable oil.
Add the beef strips and let marinate in the refrigerator for about an hour. When you're ready to cook, take the bowl out of the refrigerator and let the meat come to room temperature.
In a skillet over medium-high heat, heat 1 1/2 TBLS of remaining oil until shimmering.
Add the beef, sauté it to desired doneness.
When done, remove from the pan and set aside.
In the same skillet, add remaining 1 1/2 TBLS oil and sauté the onions and Hatch Chiles until the onions are softened, about 5 minutes.
Preheat the oven to broil.
Divide the cheese slices on the bottoms of the 4 rolls, toast in the boiler, with the tops, until cheese just begins to melt and the tops of the buns are light golden brown.
Remove the rolls from the oven and divide the meat evenly on top of the cheese. layer on the onions and Hatch Chiles.
Place avocado slices on the chiles and put toasted buns on top.