Preheat the oven to 375°F (190°C).
Place the turkey breast on a baking sheet. Drizzle with olive oil and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Rub the seasoning evenly over the turkey.
Roast the turkey in the preheated oven for 50 to 60 minutes, or until the internal temperature reaches 165°F (74°C). Remove from oven and let rest for 10 minutes before slicing.
While the turkey roasts, place the diced potatoes in a medium pot and cover with water. Bring to a boil over high heat, then reduce to medium and cook until potatoes are tender, about 15 minutes.
Drain the potatoes and return them to the pot. Add the milk, 2 tablespoons butter, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Mash until smooth and creamy. Cover and keep warm.
In a medium saucepan, combine baby carrots, honey, and 1 tablespoon butter. Add 1/4 cup water and cover. Cook over medium heat until carrots are tender and glazed, about 10 minutes. Stir occasionally.
To make the gravy, in a small saucepan, melt 1 tablespoon butter over medium heat. Whisk in 1 tablespoon flour and cook for 1 minute.
Gradually whisk in the 1/4 cup chicken broth, stirring constantly until the gravy thickens, about 3-5 minutes. Remove from heat.
Serve sliced turkey breast with mashed potatoes, glazed carrots, and drizzle with the homemade gravy.