Boil the potatoes in a large pot of salted water until fork-tender, which should take about 15 minutes.

Mash the cooked potatoes with 2 tablespoons of butter, heavy cream, and milk until smooth. Season with salt and pepper to taste, and set aside to keep warm.

Heat olive oil in a skillet over medium-high heat; cook the shrimp for 2–3 minutes per side until they turn pink and are opaque. Remove the shrimp from the skillet and set aside.

Melt the remaining butter in the same skillet; sauté minced garlic for about 1 minute until fragrant but not burnt.

Combine the heavy cream and chicken broth into the skillet; let it simmer for 3–4 minutes, allowing the flavors to meld and thicken slightly.

Stir in the grated Parmesan cheese until it’s melted and incorporated into the sauce.

Return the cooked shrimp back to the skillet, tossing them in the creamy sauce until they're well-coated and heated through.

Serve the creamy shrimp over the fluffy mashed potatoes; garnish with fresh parsley.