Butter the bottom and sides of a 13x9-inch casserole dish with 1 tablespoon softened butter. Set aside.
Cube the potatoes and place into a large pot or saucepan. Cover with cold water, adding 1 teaspoon of salt. Bring to a boil and cook the potatoes in the salted water until fork tender. Around 15 minutes. Drain well.
In a small saucepan melt together the half and half and 1/2 cup butter over medium heat, just until the butter has melted, don't boil. Remove from the heat.
To the drained potatoes add the cream cheese, garlic salt and black pepper. Using an electric mixer on medium speed, whip just to blend, they will be lumpy at this point.
Gradually add the half and half-butter mixture on medium speed, Continue to whip until smooth. Taste and adjust the salt and pepper to your taste. (The potatoes should feel soft, and will firm as they chill.)
Stir in 2 cups shredded white cheddar cheese by hand until evenly distributed.
Pour mashed potato mixture into the buttered casserole dish. Sprinkle with the remaining 1 cup shredded cheddar cheese. Dot the top with remaining 2 Tbsp butter. (Cover with plastic wrap and chill in the fridge, when making in advance.)
Bake: Remove from the fridge and bring to room temperature. Preheat the oven to 350°F. Bake for 40-45 minutes until heated through and the top is golden brown.
Serve immediately.
Cook's Note: If baking from cold, increase the baking time by 10-15 minutes.