Prepare the Grits and Greens: Stir together milk and grits in a double boiler. Using a small wire-mesh strainer, skim any hulls that float to the top of the milk. (This ensures there will be no hard bits in your creamy finished product.) Cook over medium-high, whisking often to ensure grits don’t stick to sides and bottom of pan, until milk is completely absorbed and grits are thickened and tender, 25 to 40 minutes. Stir in 1 tablespoon of the butter and 1 1/2 teaspoons of the salt. Remove from heat.

Preheat oven to 400°F. Cut and discard tough ends from turnip greens; slice stems and leaves into 1 1/2-inch pieces. Heat oil and remaining 1 tablespoon butter in a 12-inch cast-iron skillet until butter melts. Add garlic, and cook, stirring occasionally, just until garlic starts to sizzle. (Be careful garlic does not start to turn brown and burn.) Add greens, red pepper, and remaining 1 teaspoon salt. Using tongs, toss greens until they are just wilted. Add greens mixture and any accumulated liquids to grits in double boiler. Add cheese, stock, and black pepper; stir to combine.

Spoon grits mixture into the same skillet. (Do not wipe skillet clean.) Bake uncovered until set, about 30 minutes.

Prepare the Hot Sauce: Melt butter in an 8-inch skillet over medium until it starts to foam and turn slightly brown. Stir butter to distribute evenly on bottom of skillet, and cook, undisturbed, until butter browns and smells nutty. Stir in lemon juice, hot sauce, and salt. Cook, undisturbed, until bubbly, about 15 seconds. Spoon sauce over baked grits.