Place potatoes and 1 tablespoon kosher salt into a large pot and cover with water; bring to a boil. Reduce heat to medium-low, cover, and simmer until tender, 25 to 35 minutes. Drain and transfer potatoes to a large bowl.
Mix half-and-half and butter in a small saucepan over medium-low heat until heated through and butter is melted, 5 to 10 minutes.
Blend potatoes with an electric hand mixer in the large bowl until mashed. Slowly pour 3/4 the cream-butter mixture into blended potatoes; mix on lowest speed until fully incorporated. Fold in the remaining 1/4 cream-butter mixture and sour cream. Season with 2 teaspoons kosher salt and black pepper.
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