Peel the potatoes if desired and cut them into evenly sized chunks so they cook at the same rate.
Place the potatoes in a large pot, cover with cold salted water, and boil for 15–20 minutes until fork-tender.
Pat the chicken breasts dry and gently pound thick pieces to an even thickness.
Season both sides of the chicken evenly with ranch seasoning, garlic powder, paprika, and black pepper.
Heat olive oil in a large skillet over medium-high heat until hot.
Sear the chicken for 4–5 minutes per side until golden, then transfer it to a clean plate.
Drain the potatoes well and let them sit briefly in the hot pot so excess moisture evaporates.
Mash the potatoes with butter, warm milk, salt, and black pepper until creamy, adding a little more milk if needed.
Reduce the skillet heat to medium, pour in chicken broth, and scrape up the browned bits from the bottom.
Stir in the heavy cream, remaining ranch seasoning, and Parmesan until the cheese melts into the sauce.
Simmer the sauce gently for 2–4 minutes until slightly thickened, avoiding a hard boil.
Return the chicken to the skillet and spoon the creamy ranch sauce over each piece.
Cover and simmer for 6–10 minutes until the chicken reaches 165°F (74°C) in the thickest part.
Adjust the sauce with a splash of broth or milk if too thick, or simmer uncovered briefly if it needs to thicken.
Taste the sauce before adding salt because ranch seasoning and Parmesan can already be salty.
Let the chicken rest in the sauce for 3–5 minutes.
Spoon mashed potatoes onto each plate, place the chicken over or beside them, and spoon plenty of ranch sauce on top.
Garnish with parsley or extra Parmesan if desired and serve immediately.