Season chicken breasts uniformly on both sides with steak seasoning and garlic powder.
Heat olive oil in a large heavy-bottomed skillet over medium-high heat until shimmering.
Place chicken in the skillet and sear for 6-7 minutes per side until the internal temperature reaches 165°F (74°C).
Remove chicken from the skillet and tent loosely with foil to retain heat.
In the same skillet, melt the butter and add the sliced onions and mushrooms.
Sauté the vegetables over medium heat for 8-10 minutes, stirring occasionally, until the onions are translucent and the mushrooms are golden brown.
Season the vegetable mixture with salt.
Return the chicken breasts to the skillet, placing them directly onto the pan surface or atop the vegetables.
Distribute the sautéed onion and mushroom mixture evenly over each chicken breast.
Top each breast with approximately 0.375 cups of shredded Monterey Jack cheese.
Cover the skillet with a lid for 2 minutes or place under a broiler for 60-90 seconds until the cheese is fully melted and bubbling.
Serve immediately.