Heat the olive oil in a large pot over medium heat. Add the lamb cubes and brown them on all sides. Remove the lamb and set it aside.
Add the onion, carrots, and garlic to the same pot. Cook for 5 minutes until the onion softens.
Sprinkle the flour over the vegetables and stir for 1 minute. Slowly pour in the broth while stirring to avoid lumps.
Return the lamb to the pot. Add the thyme, salt, and pepper. Bring to a simmer, cover, and cook for 1 hour until the lamb is tender.
While the stew simmers, place the potatoes in a saucepan and cover with water. Boil until soft, then drain. Mash with the milk and butter until smooth.
Stir the peas into the finished stew and cook for 3 more minutes. Transfer the stew to a baking dish.
Spread the mashed potatoes evenly over the top. Bake at 375°F for 15 minutes until the topping starts to turn golden.