Place 3/4 cup butter into the freezer for 1 hour. Cut into cubes.

Preheat the oven to 425 degrees F (220 degrees C).

Combine flour, 1/3 cup sugar, baking powder, baking soda, and salt in a large bowl using a whisk. Cut in very cold cubed butter with a pastry blender or using your fingers until you get coarse crumbs.

Create a well in the flour mixture; add buttermilk and stir gently until dough is just moistened. Fold in cinnamon chips.

Turn dough out onto a lightly floured surface. Knead gently until dough is no longer sticky, 10 to 12 times, and divide in half. Pat or roll each portion gently into a 7-inch circle. Brush melted butter over circles. Sprinkle each with 1 tablespoon sugar. Cut each circle into 6 wedges. Separate and place scones on an ungreased baking sheet.

Bake in the preheated oven until lightly browned, 10 to 13 minutes. Serve warm.