Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Toss potatoes with butter in a microwave-safe bowl. Microwave on high power for 8 minutes.
Place cream cheese into the bottom of a large bowl. Pour hot potatoes on top and mix gently until only a few lumps are left.
Heat milk in a microwave-safe container in a microwave until warm, 30 to 45 seconds. Stir gently into potato mixture until well combined. Add eggs and stir well. Stir in tomato, onion, cilantro, garlic salt, pepper, and marjoram. Fold in Cheddar cheese gently. Pour into the prepared pan.
Bake in the preheated oven until set and golden, about 45 minutes.