Bring a large pot of salted water to a boil. Add halved potatoes and cook until fork-tender, 8 to 12 minutes. Drain and set aside.
Melt butter in a large skillet over medium heat. Add shallots and garlic, and saute for 1 to 2 minutes.
Reduce heat to low, pour in cream and Parmesan cheese, and stir to combine. Simmer gently, stirring constantly, until it starts to thicken, about 4 minutes. Stir in lemon pepper until well combined. Taste, and adjust seasoning, to suit your preference.
Add potatoes to skillet, and gently toss until well coated in the sauce. Sprinkle with parsley, and serve.