Prepare a grill fire to 350° using hickory or oak for smoke flavor.
Pat steak dry with paper towels. Coat with olive oil and season with beef rub or steak rub on both sides.
Cook over a hot grill fire with the grill closed for 5 minutes. Flip the steak and continue to cook until desired doneness. We cooked ours to 135° using a digital meat thermometer.
Remove steak from grill and place on a rimmed baking sheet. Cover with foil and rest while you cook the onions and green chile sauce.
Slice onion thin and cook with olive oil over medium-high heat, stirring occasionally until caramelized.
In a saucepan, melt butter and whisk in flour. Cook 2 minutes.
Add garlic, cumin and salt.
Whisk in sour cream and milk. Add green chiles with juice.
Add Worcestershire sauce and horseradish, whisking to combine. Continue to cook until sauce is thickened. Remove from heat.
Slice the steak into thin slices.
MAKE THE SLIDERS
Preheat oven to 400°.
Slice slider buns in half and place the bottoms onto a lined baking sheet.
Spoon green chile sauce over the slider buns.
Top with caramelized onions.
Add a layer of sliced steak.
Drizzle more green chile sauce over the steak.
Top with shredded cheese.
Cook sliders, open faced for 5- 8 minutes or until cheese is melted.
Remove from oven and place the top side of the slider buns over the sandwiches.
Brush with melted butter and sprinkle with everything bagel seasoning.
Bake for 5 minutes or until buns are lightly toasted.
Slice sandwiches apart and serve immediately.