Start by steaming the broccoli until it's tender. Pour one inch of water into a medium saucepan and bring it to a simmer. Place a medium sieve in the pot and add the broccoli. Cover tightly with the lid and steam for about 3 minutes, or until the broccoli turns bright green and can be easily pierced with a fork.
In a large bowl, mix together the steamed broccoli, eggs, cheddar, flour, garlic powder, paprika, onion powder, salt, and pepper. Stir until everything is well combined.
With clean hands, shape the mixture into 6 large fritters, each about 3 inches wide and 3/4 inch thick.
For frying: Heat a large non-stick skillet over medium-high heat and add enough oil to cover the bottom. Once the oil is hot, place 3-4 fritters in the pan. Cook each side for about 3 minutes, or until golden brown. Transfer the fritters to a plate lined with paper towels to drain the excess oil.
For baking: Preheat your oven to 350°F. Line a baking sheet with parchment paper and arrange the fritters evenly. Bake for 30 minutes, flipping them halfway through to ensure even cooking.
Serve the fritters with a dollop of sour cream, plain Greek yogurt, or ranch dressing.