In a mixing bowl, combine the softened butter with chopped rosemary, thyme, minced garlic, salt, pepper, lemon zest, and lemon juice. Mix until well incorporated and fragrant.
Pat the turkey breast dry with paper towels. If using bone-in, gently loosen the skin without detaching it completely to allow herb butter infusion.
Spread half of the herb butter mixture underneath the skin or evenly over the turkey breast surface. Rub the remaining butter all over the outside. Drizzle olive oil on top.
Preheat oven to 375°F (190°C). Place turkey breast skin-side up in a roasting pan or baking dish. Roast uncovered for 1 hour 15 minutes to 1 hour 30 minutes until internal temperature reaches 165°F (74°C).
Remove from oven and tent loosely with foil. Let rest for 10-15 minutes before slicing to retain juices. Slice and serve.
