Preheat the oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Whisk together the flour, granulated sugar, baking powder, salt, and cinnamon. Cut in the cold butter until the mixture is crumbly with some pea-sized pieces of butter remaining.
In a separate bowl, whisk the egg, 3/4 cup heavy cream, and vanilla. Add to the flour mixture and gently stir just until a shaggy dough forms. Add a little extra cold cream only if the dough is too dry to come together.
Turn the dough onto a lightly floured surface and gently shape it into a rectangle. Spread the softened butter over the dough, leaving a small border around the edges. Mix the brown sugar, cinnamon, and salt together, then sprinkle evenly over the butter.
Fold one short side of the dough toward the center, then fold the opposite side over it like a letter. Gently press the dough together, then shape it into a round about 1 inch thick. Cut into 8 equal wedges.
Arrange the scones on the prepared baking sheet about 2 inches apart. Brush the tops lightly with heavy cream and refrigerate for 20 minutes.
Bake for 18-22 minutes, until the tops and edges are golden and the centers are cooked through. Let the scones cool on the pan for 5 minutes, then transfer to a wire rack for another 10-15 minutes.
Beat the softened cream cheese until smooth. Whisk in the confectioners' sugar, vanilla, salt, and 1 tablespoon milk or cream. Add additional milk 1 teaspoon at a time until the glaze reaches your preferred consistency. Drizzle over the slightly warm scones and serve.