Preheat your oven to 400°F (200°C) and grease a baking sheet or line it with parchment paper.
In a large mixing bowl, combine the flour, baking powder, and salt. Mix well.
Add the melted butter and milk to the dry ingredients, stirring until just combined. Do not overmix.
Fold in the diced ham, shredded cheddar cheese, chopped green onions, garlic powder, and black pepper until evenly distributed.
Turn the dough out onto a floured surface and knead gently for about 1 minute until it comes together.
Roll the dough into a rectangle about 1/2 inch thick. Cut into strips approximately 2 inches wide.
Roll each strip up tightly and place seam-side down on the prepared baking sheet.
Bake in the preheated oven for 15-20 minutes, or until golden brown.
Allow to cool slightly before serving.