Melt 4 tablespoons of butter in a 10-inch non-stick skillet over medium-low heat. Add the potatoes and fry them until cooked through, about 15 minutes.
Melt the remaining 4 tablespoons of butter in a small dish in the microwave. Whisk the eggs, then stir in goat cheese, melted butter, salt, pepper, and herbs.
Pour the egg mixture over the potatoes and cook the frittata, without stirring, for 15 minutes, or until the edge is set but the center is still soft. Sprinkle the diced tomatoes over the top. Broil the frittata about 4 inches from the heat for 4 to 5 minutes, run a thin knife around the edge, and slide the frittata onto a serving plate.