Preheat your oven to 375°F (190°C) to ensure that it’s hot and ready for your frittata.
In a medium saucepan, combine the broccoli florets and water. Bring to a boil and cook for about 3-4 minutes until the broccoli is bright green and slightly tender. Drain and set aside.
In a mixing bowl, whisk together the 6 eggs, 1 tablespoon of milk, 1/2 teaspoon of salt, and 1/4 teaspoon of black pepper until smooth and fully combined.
Stir the cooked broccoli, 1 cup of grated aged sharp cheddar, 2 tablespoons of chopped fresh dill, and 1/2 teaspoon of smoked paprika into the egg mixture until everything is evenly distributed.
In your oven-safe skillet, heat a bit of oil over medium heat. Pour the egg and broccoli mixture into the skillet, cooking for about 3-4 minutes until the edges begin to set.
Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the frittata is puffed and the center is set. A toothpick inserted in the middle should come out clean.
Once baked, remove the frittata from the oven and allow it to cool for a few minutes before slicing. Serve warm or at room temperature, garnished with additional dill if desired.