Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a large bowl, whisk together flour, baking powder, sugar, garlic powder, salt, and paprika.
Cut in cold butter with a pastry cutter or fork until mixture looks like coarse crumbs.
Stir in cheddar cheese.
Pour in milk and gently mix until dough comes together (do not overmix).
In a medium bowl, combine crab meat, mayonnaise, cream cheese, Dijon, lemon juice, green onion, Old Bay, and black pepper. Stir until well combined.
Scoop about 2 tablespoons of dough and flatten slightly in your hand. Place 1 tablespoon of crab filling in the center.
Fold dough around filling and pinch edges closed. Place seam-side down on prepared baking sheet. Repeat with remaining dough and filling.
Place biscuits in preheated oven and bake 18–20 minutes, until golden brown on top.
In a small bowl, whisk together melted butter, lemon juice, garlic powder, and parsley.
Brush hot biscuits generously with lemon butter topping. Serve warm.