Place the potato chunks in a large pot, cover with cold salted water, and bring to a boil. Cook for 15 to 20 minutes, until very tender.

While the potatoes cook, season the chicken breasts with 1 teaspoon salt, 1/2 teaspoon black pepper, paprika, and flour, coating lightly on both sides.

Heat the olive oil in a large skillet over medium-high heat. Sear the chicken for 4 to 5 minutes per side, until golden brown and mostly cooked through. Transfer to a plate.

Reduce the heat to medium and add the butter to the same skillet. Stir in the minced garlic and cook for 30 to 60 seconds, just until fragrant.

Pour in the chicken broth and scrape up any browned bits from the pan. Stir in the heavy cream, Parmesan cheese, Italian seasoning, remaining salt, and remaining black pepper.

Return the chicken to the skillet and simmer for 6 to 8 minutes, spooning the sauce over the chicken, until the chicken is fully cooked and the gravy has thickened.

Drain the potatoes and return them to the pot. Add the butter and warm milk, then mash until smooth and creamy. Season with salt and pepper to taste.

Serve the creamy garlic chicken over the mashed potatoes, spoon extra gravy on top, and garnish with chopped parsley.