Preheat the oven to 400°F (200°C). Line a large baking sheet with parchment paper.
Add the flour, baking powder, sugar, garlic powder, salt, and paprika to a large mixing bowl. Whisk until evenly combined.
Add the cold cubed butter. Use a pastry cutter, fork, or your fingertips to work it into the flour until the mixture resembles coarse crumbs with some small pieces of butter remaining.
Stir in the shredded sharp cheddar.
Pour in the milk or buttermilk and gently mix just until a soft biscuit dough forms. Avoid overworking the dough.
Prepare the filling by combining the drained crab meat, mayonnaise, softened cream cheese, Dijon mustard, lemon juice, green onion, seafood seasoning, and black pepper in a separate bowl. Stir gently until combined.
Scoop approximately 2 tablespoons of biscuit dough and gently flatten it in your palm.
Place about 1 tablespoon of crab filling in the center. Carefully bring the dough up and around the filling, then pinch the edges together to completely seal it inside.
Place the stuffed biscuit seam-side down on the prepared baking sheet. Repeat with the remaining dough and filling.
Bake the Crab Stuffed Cheddar Bay Biscuits with Lemon Butter for 18–20 minutes, or until puffed and beautifully golden brown.
While the biscuits bake, combine the melted butter, lemon juice, garlic powder, and chopped parsley in a small bowl.
Remove the biscuits from the oven and immediately brush the tops generously with the warm lemon garlic butter.
Let them cool for a few minutes before serving warm.