Preheat the oven to 400°F (200°C) and place a rack in the middle position.
In a medium mixing bowl, beat 6 eggs with 1 tablespoon milk, 1/2 teaspoon salt, and 1/4 teaspoon black pepper until combined and slightly fluffy. Set the egg mixture aside.
In a medium saucepan combine 2 cups broccoli florets and 1/2 cup water. Bring to a boil over high heat, cover, and steam about 4 minutes, until the broccoli is bright green and tender.
Drain the broccoli in a colander and shake off excess water. Pat the broccoli dry with a clean kitchen towel or paper towel if needed to remove surface moisture.
Lightly grease an oven-safe skillet. Spread the drained broccoli in an even layer across the bottom of the skillet.
Sprinkle 1 cup grated aged sharp cheddar evenly over the broccoli.
Add 2 tablespoons chopped fresh dill to the reserved egg mixture and whisk briefly to incorporate.
Pour the egg-and-dill mixture evenly over the broccoli and cheese, tilting the skillet as needed so the eggs cover the ingredients.
Cook the skillet over medium heat on the stovetop for about 2 minutes, until the edges of the eggs begin to set and brown slightly.
Sprinkle 1/2 teaspoon smoked paprika lightly over the top of the eggs.
Carefully transfer the skillet to the preheated oven and bake about 10 minutes, until the center is set and a knife inserted into the center comes out clean.
Remove the frittata from the oven and let it rest for a few minutes before slicing. The frittata will be puffed when hot and will settle as it cools.
Notes
NOTES
You will also need
: medium saucepan with lid, 10-inch seasoned cast iron skillet or nonstick skillet with oven safe handle, nonstick cooking oil spray or olive oil.