Preheat the oven to 350℉.
Cut the potatoes into 2-inch chunks by cutting in half lengthwise, then cut each half into thirds.
Add them to a pot of cold, salted water so they are completely submerged. Turn the burner on high to start cooking the potatoes.Once boiling, they will take about 20 minutes to cook. You might need to reduce the burner to medium-high to prevent the water from boiling over the pot. While the potatoes are cooking, add the cream cheese, butter, sour cream, and kosher salt to a large mixing bowl.
Check the potatoes to see if they are done. They need to be very soft. A fork will easily pierce multiple potatoes.Drain into the colander over the sink. Let the potatoes sit for 3 minutes to dry out. Place the potatoes in the mixing bowl of the stand mixer. Slowly blend the ingredients only using the lowest setting with the paddle attachment for 1-2 minutes. Or, mash by hand with a potato masher until blended.
Taste the potatoes for seasoning. Observe the texture. If they are firm, add the half and half (1 tablespoon at a time) and mix by hand with a spatula. If the texture is loose or somewhat watery, do not add the half and half.
Spoon and smooth the mixture into a lightly greased baking dish. Do not wipe the paddle attachment because it will have some fibrous pulp on it.Pinch the butter into 12 small pieces and drop on top of the mashed potatoes. Sprinkle the paprika. Bake, uncovered, for about 30 minutes until the center is hot, at 180℉, and the top has browned. Serve within 30 minutes.