Whisk together the flour, baking powder, and salt. Stir in the cheddar cheese, and diced jalapeños. Cut the stick of butter into 8 pieces and then work the butter into the flour mixture with your hands or a pastry blender until the flour is crumbly. Stir in the half-and-half, mixing until the dough is well combined. It’s okay if the dough is a little sticky.