Heat the oven to 425°F. Lightly grease an 8 x 8-inch baking pan and set aside.
In a large bowl, whisk together the flour, 1 tablespoon brown sugar, baking powder, 1 teaspoon of cinnamon, and salt, breaking up any large clumps in the brown sugar. Pour in 1 1/2 cups of the cream and mix just until combined. Dump the dough onto a lightly floured surface and pat into a long, thick rectangle. The dough will be firm, yet wet and sticky.
Slice the rectangle into 8 equally-sized squares. Lay four of the squares in the prepared baking pan. Sprinkle the remaining 2 tablespoons of brown sugar, 1/2 teaspoon cinnamon, and half of the cinnamon chips over each square. Place the remaining biscuit dough squares on top and lightly press the edges to seal. Top the biscuits with the remaining cinnamon chips.
Bake for 14 to 16 minutes, or until the biscuits are slightly golden brown on the outside and just cooked through. Remove from the oven and use a knife to spread and smear the hot cinnamon chips on top of the biscuits.
Whisk together the remaining 1/2 cup cream, confectioner's sugar, and vanilla extract. Lightly drizzle the biscuits with this glaze. Serve immediately.