Place the Yukon Gold potatoes in a large pot of salted water. Bring to a boil and cook for 15–20 minutes, or until fork-tender.
Drain the potatoes thoroughly and return them to the pot. Add butter, heavy cream, and salt. Mash until smooth and creamy. Cover and keep warm.
Heat 1 tablespoon butter in a large skillet over medium heat.
Season the shrimp with salt and black pepper. Cook for about 2 minutes per side until pink and opaque. Remove from the skillet and set aside.
Add the remaining butter to the skillet. Stir in the minced garlic and sauté for about 1 minute until fragrant.
Pour in the chicken broth and simmer for 2 minutes, scraping up any browned bits from the pan.
Stir in the heavy cream and red pepper flakes. Simmer for 4–5 minutes until the sauce begins to thicken.
Add the Parmesan cheese, if using, and stir until melted and smooth.
Mix in the chopped parsley.
Return the shrimp to the skillet and gently coat them in the sauce. Simmer for another 2 minutes until heated through.
Spoon the creamy mashed potatoes onto serving plates and top generously with the Creamy Garlic Shrimp Over Mashed Potatoes mixture. Garnish with additional parsley and freshly cracked black pepper if desired.