Preheat the oven to 350°F (175°C).

Prepare the lobster tails by cutting through the top shell lengthwise, stopping just before the tail fin. Pull the meat out and recline it on top of the shell. Place the lobster tails in a baking dish.

In a small saucepan, melt the butter over medium heat. Add minced garlic and sauté until fragrant, about 1 minute. Remove from heat and stir in lemon juice, parsley, thyme, salt, and pepper.

Brush the garlic herb butter mixture generously over the lobster meat. Reserve some butter for drizzling before serving.

Bake the lobster tails in the preheated oven for about 15-20 minutes or until the meat is opaque and cooked through.

While the lobster is baking, peel and chop the potatoes. Place them in a large pot and cover with water. Bring to a boil and cook until tender, about 15-20 minutes.

Drain the potatoes and return them to the pot. Add milk, olive oil, salt, and pepper. Mash until smooth and creamy.

Once the lobster tails are done, remove them from the oven and drizzle with any leftover garlic herb butter. Let them cool slightly.

Serve the lobster tails alongside a generous helping of mashed potatoes. Garnish with additional parsley if desired.