Preheat the oven to 375°F (190°C). Set a standard muffin tin on the counter — we'll use it to steady the split English muffins while baking.
Cook the bacon: heat a skillet over medium and add the bacon slices. Fry until crisp, about 6–8 minutes, turning as needed. Transfer to a paper towel-lined plate, then chop into bite-size pieces. If using the oven, bake at 400°F on a sheet until crispy, about 12 minutes.
Lightly toast the English muffin halves until just golden (use a toaster or oven). Use a small spoon to gently hollow out some of the soft center from each half to create a shallow cup — save the crumbs for another use.
Place each muffin half upright in the muffin tin cups so they stand stable. If desired, brush the cut surfaces with a little olive oil to help them brown.
Whisk eggs in a bowl with the milk, salt, pepper, smoked paprika, and most of the chives (reserve a pinch for garnish). Beat until smooth and slightly frothy to make the filling light.
Divide the chopped bacon evenly among the muffin cups, then pour the egg mixture into each muffin until nearly full (leave a little room for expansion). Sprinkle the shredded cheddar on top of each filled muffin.
Bake in the preheated oven until the eggs are set but still tender, about 12–15 minutes. For a golden, bubbling top, switch the oven to broil for 1–2 minutes—watch closely to avoid burning.
Let the stuffed muffins rest in the tin for 2 minutes, then carefully lift them out with a thin spatula. Garnish with the remaining chives and serve warm with hot sauce or salsa if you like.
To reheat later: warm in a 325°F oven for 8–10 minutes or microwave on medium power for 45–60 seconds.