Season the Lamb: Pat the lamb chops dry with paper towels, then season both sides generously with salt, black pepper, garlic powder, and paprika. Let them sit at room temperature for 5 minutes to allow the seasonings to adhere.
Sear the Chops: Heat olive oil in a large skillet over medium-high heat until shimmering, about 2 minutes. Carefully place the lamb chops in the pan and sear for 3-4 minutes on each side for medium-rare doneness, adjusting time based on thickness and your preference.
Create the Garlic Glaze: Remove the lamb chops to a plate and reduce heat to medium. Add minced garlic to the same skillet with 2 tablespoons butter, stirring constantly for 1-2 minutes until fragrant and golden, being careful not to burn the garlic.
Coat the Chops: Return the lamb chops to the skillet and turn to coat both sides with the garlic butter glaze, cooking for an additional 1-2 minutes. Remove from heat and garnish with fresh parsley.
Prepare the Potatoes: Bring a large pot of salted water to a boil, add cubed potatoes, and cook for 12-15 minutes until fork-tender. Drain completely, return to the pot, and mash with butter and milk until smooth and creamy, seasoning with salt and pepper to taste.
Steam the Broccoli: In a steamer basket over boiling water, steam broccoli florets for 5-7 minutes until bright green and tender-crisp. Season with salt and pepper.
Roast the Squash: Toss butternut squash cubes with a light coating of olive oil, salt, and pepper. Roast on a baking sheet at 400 degrees Fahrenheit for 15-18 minutes, stirring halfway through, until caramelized and tender.
Plate the Dish: Spoon a generous portion of creamy mashed potatoes into the center of each plate, lean one or two lamb chops against the potatoes, and arrange steamed broccoli and roasted butternut squash around the base. Drizzle any remaining garlic butter over the entire plate and garnish with additional fresh parsley.