Melt the butter; set aside to cool. Line two cookie sheets with silicone liners or parchment paper.
Whisk together the flour, sugar, salt, baking powder, cinnamon, and cinnamon chips together in a large bowl.
In a small bowl, whisk together the egg, vanilla, and half & half. Stir the melted, cooled butter into the cream mixture. It should form small clumps.
Add the wet ingredients to the flour mixture. Stir gently just until combined, pressing the dough together into a ball.
Divide the dough in half. Press each portion into a 7" circle on a lightly floured surface. Cut into 8 wedges with a sharp knife, bench scraper, or pizza cutter.
Place 8 scones on each prepared baking sheet, at least 2 inches apart. Chill the scones while you preheat your oven to 425°.
Use a pastry brush to spread milk over the top of each scone. Bake in a preheated oven at 425 degrees for about 15 minutes, or until golden brown.
Let the scones cool for at least 10 minutes before adding the icing.
For the icing - Whisk together all the ingredients, adding enough cream to get a thin, smooth consistency. Drizzle over the tops of the scones.