Slice the pork loin into ½–¾ inch thick pieces. Season both sides with salt, pepper, garlic powder, and onion powder. Heat butter or oil in a large skillet over medium heat. Sear the pork until golden on both sides and fully cooked. Remove from the pan and let rest.
In the same skillet, add the sliced onion and cook until softened and lightly golden. Add the mushrooms and cook until tender and lightly browned.
Slice the rested pork very thin, cutting against the grain, then give it a light chop for smaller, easy-to-eat pieces. Return the pork to the skillet with the mushrooms and onions. Add the broth or water, cover, and simmer on low for 5–7 minutes, until the mixture is soft and scoopable.
Preheat oven to 375°F (190°C). Brush bagel halves with melted butter and sprinkle lightly with garlic powder and onion powder. Bake for 8–10 minutes, just until lightly golden. Do not over-toast.
Place the bottom half of each bagel on a baking sheet. Spoon the pork and mushroom mixture evenly over each one. Top with Velveeta slices. Return to the oven for 3–5 minutes, until the cheese is fully melted.
Remove from the oven and gently place the top bagel halves on. Serve warm.