Trim and slice whites of green onions into 1/2" pieces. Thinly slice remaining green onions on an angle. Halve grape tomatoes. Zest lemon, halve, and juice. Rinse shrimp, pat dry, and season with a pinch of salt and pepper.

When water is boiling, whisk in grits in a steady stream to avoid clumping. Stir until consistency is slightly thicker than pancake batter. Reduce heat to medium-low and cook 2 minutes. Stir in 1 Tbsp. butter and smoked Gouda. Season to taste with salt and pepper. Remove from heat and keep warm.

Place a large pan over medium-high heat and add 1 tsp. olive oil. Add shrimp and sear on one side until browned, about 2 minutes, then remove to a plate (shrimp will finish cooking later). Reserve pan for next step (no need to wipe clean).

Return pan to medium heat and add remaining butter. Allow butter to melt, then continue cooking until it begins to smell nutty and turn golden, about 3 minutes. Butter browns shortly after it stops sizzling, so listen closely for when it's ready. Stir in white parts of green onions, mustard, lemon zest, 1 Tbsp. lemon juice, red pepper flakes (start with a 1/4 tsp., taste, and add more, if desired), and a pinch of salt and pepper. Return shrimp to pan and cook 2 minutes or until shrimp is opaque and reaches a minimum internal temperature of 145 degrees.

In a medium mixing bowl, combine 2 tsp. lemon juice, 1 Tbsp. olive oil, and salt and pepper (to taste). Stir, add arugula and tomatoes, and toss together.

Divide grits between two shallow bowls and sprinkle with smoked paprika (to taste). Add shrimp, spoon butter sauce over grits, and garnish with remaining green onions. Serve arugula and tomato salad on side.