Heat the olive oil in a large skillet over medium heat. Add the chicken breasts and season with salt and pepper. Cook until golden brown on both sides and cooked through, about 10-15 minutes.
Remove the chicken from the skillet and set aside. In the same skillet, melt the butter and add the minced garlic. Sauté for 1-2 minutes until fragrant.
Add the chicken broth to the skillet, bring to a simmer, and let it reduce slightly while stirring occasionally, about 5-7 minutes.
Meanwhile, boil the diced potatoes in salted water until tender, about 15 minutes. Drain and return them to the pot.
Add the milk, cheddar cheese, salt, and pepper to the potatoes. Mash until desired creaminess is reached.
Slice the cooked chicken and return to the skillet, coating it in the gravy. Serve immediately with cheesy mashed potatoes.
Notes
Tip: For extra flavor, you can add herbs like thyme or rosemary to the gravy.