Preheat the oven to 375°F (190°C) and grease a muffin tin or line it with paper liners.
In a medium bowl, combine the chopped broccoli and shredded cheddar cheese. Set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, black pepper, garlic powder, and onion powder.
In another bowl, mix the milk, vegetable oil, and eggs until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Gently fold in the broccoli and cheese mixture until evenly distributed.
Divide the batter evenly among the muffin cups, filling each about 2/3 full.
Bake for 20-25 minutes or until the muffins are golden brown and a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.