Preheat oven to 425 degrees.
Slice off the top of the head of garlic. Wrap garlic in aluminum foil and roast for 35 minutes. Remove from oven when tender and turn the oven down to 375 degrees.
Meanwhile, place potatoes in a pot of cold salted water. Bring to a boil. Cook until fork-tender and mash until nearly smooth.
Squish out the roasted garlic from its skins and mash in a small saucepan. Add milk and half of the butter and place over medium heat. When butter melts, stir the mixture into potatoes.
Set a large skillet over a medium-high flame. Add olive oil and when it shimmers, add onions, carrots, and thyme and cook until onion is translucent. Add meat, season with salt and pepper, and cook, stirring until browned.
In a medium saucepan over medium heat, heat the remaining 2 ounces of butter. Whisk flour into melted butter and cook for a few minutes, then add tomato paste. Whisk in stock and Worcestershire sauce. Cook a few minutes until thickened. Season with salt and pepper and then remove from heat.
Stir half of this gravy into the meat mixture, along with peas. Turn mixture into a buttered 3-quart casserole dish and spoon garlic mashed potatoes on top. Dust with paprika. Bake for 20 minutes, until bubbling and slightly browned. Serve hot with remaining gravy alongside.