Preheat your oven to 400°F (200°C). Grate the Russet potatoes using the large holes of a box grater. Place the grated potatoes in a clean kitchen towel or cheesecloth and squeeze out as much moisture as possible. This is a crucial step to ensure the muffins hold their shape and become crispy.

In a small skillet, heat a drizzle of olive oil over medium heat. Add the finely chopped red onion and sauté for 2-3 minutes until softened. Add the finely chopped broccoli florets and cook for another 3-4 minutes until they are bright green and slightly tender. Remove from heat and let cool slightly.

In a large mixing bowl, combine the squeezed grated potatoes, sautéed broccoli and onion, shredded cheddar cheese, and the cooled melted butter.

Pour the beaten eggs into the potato mixture. In a separate small bowl, whisk together the all-purpose flour, garlic powder, smoked paprika, salt, pepper, and cayenne (if using). Add the flour mixture to the potato mixture and stir until everything is evenly coated. Finally, fold in the sour cream or Greek yogurt, mixing just until combined. Be careful not to overmix.

Grease a 12-cup standard muffin tin generously with olive oil or cooking spray. Using a large spoon or an ice cream scoop, portion the mixture evenly into each muffin cup. Press the mixture down gently with the back of the spoon to compact it.

Place the muffin tin in the preheated oven and bake for 30-35 minutes. The muffins are done when they are golden brown and crispy on the edges. A toothpick inserted into the center should come out clean.

Let the muffins cool in the tin for 5 minutes before carefully transferring them to a wire rack. Serve warm with a dollop of sour cream, a sprinkle of fresh chives, or your favorite dipping sauce.