In a medium saucepan over medium heat, boil the potatoes in lightly salted water until fork-tender, about 12 minutes.
Preheat the oven to 475F.
Place the potatoes on a baking sheet. Using a potato masher, gently press down to mash each one. The tops of the potatoes should be really textured. Drizzle the tops of the potatoes with the olive oil. Sprinkle generously with salt and pepper. Bake until golden brown and crisp, about 15 minutes. These are absolutely irresistible!
Place 1/4 pat of butter on top of each smashed potato before baking.
Top each smashed potato with grated Cheddar before baking.