1. Heat olive oil in a skillet. Season chicken breasts with salt and pepper, then sear on both sides until golden. Add 1 cup chicken broth, cover, and simmer for 20 minutes. Shred the cooked chicken using two forks.
2. In the same skillet, whisk flour into the remaining broth to create a smooth gravy. Simmer until thickened.
3. Boil potatoes in salted water until fork-tender. Drain, then mash with milk, butter, salt, and pepper until creamy.
4. Serve shredded chicken over mashed potatoes, drizzled with gravy.