Prepare the filling. Stir together the melted and cooled butter, brown sugar, and cinnamon. Set aside until it forms a spreadable paste. The filling should not be warm when added to the dough.

Mix the dry ingredients. Line a baking sheet with parchment paper. In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt.

Cut in the butter. Add the cold, cubed butter. Using a pastry cutter or your fingertips, work it into the flour until crumbly, leaving some pea-sized pieces.

Add the liquid. Combine the cold milk and vanilla, then pour into the flour mixture. Stir gently until a shaggy dough forms.

Shape the dough. Turn onto a lightly floured surface. Gently press together, folding once or twice if needed to incorporate loose crumbs. Divide into three equal portions and pat each into a circle approximately 6 inches (15 cm) across and about ⅜ inch (1 cm) thick.

Layer the scones. Spread half the cinnamon filling over the first circle, leaving a small border around the edge. Place the second circle on top and spread with the remaining filling. Top with the third circle. Gently align the edges without pressing the stack flat.

Cut and chill. Cut straight down through the stack to make eight wedges. Transfer to the prepared baking sheet, leaving about 2 inches (5 cm) between them. Refrigerate for 20 minutes. Meanwhile, preheat the oven to 425°F (220°C).

Bake. Bake on the middle rack for approximately 18–22 minutes, checking from 15 minutes onward. The tops and edges should be golden, and the exposed dough between the filling layers should look set. Loosely cover with foil if the tops brown too quickly.

Cool slightly. Let the scones rest on the baking sheet for 5 minutes, then carefully transfer to a cooling rack. Cool for another 5–10 minutes before glazing.

Glaze and serve. Whisk together the powdered sugar, vanilla, and 1 tablespoon milk. Add more milk a little at a time until thick but pourable. Drizzle over the slightly warm scones and serve.