Preheat oven to 350°F. Use a small amount of the 1 tablespoon shortening to grease 11 cavities of a muffin tin; reserve the remaining shortening for the chocolate drizzle.
Open the can of Pillsbury Grands! Blueberry Biscuits. Cut each biscuit into 4 pieces and place all pieces into a large zip-top bag.
Add 1/3 cup granulated sugar and 1/2 teaspoon of the 3/4 teaspoon cinnamon (reserve the remaining 1/4 teaspoon) to the bag with the biscuit pieces. Seal the bag and shake until the biscuit pieces are evenly coated with the cinnamon sugar.
In a microwave-safe bowl, melt 1/2 cup butter until fully liquid. Stir in 1/4 cup brown sugar and the reserved 1/4 teaspoon cinnamon until the brown sugar is dissolved and the mixture is combined.
Spoon an equal amount of the butter-brown sugar mixture into each of the 11 greased muffin cavities, using all of the butter mixture.
Divide the coated biscuit pieces evenly among the 11 muffin cavities. Press the pieces down gently so they fit into the cavities and are coated with the butter-brown sugar mixture.
Bake for 10–13 minutes, until the tops are golden and the centers are no longer doughy. Remove from the oven and let the muffins cool in the pan for about 5 minutes, then invert the pan and remove the muffins to a cooling rack or plate.
While the muffins cool, place 1/2 cup white chocolate chips and the remaining portion of the 1 tablespoon shortening in a microwave-safe bowl. Melt in short intervals (stirring between) until smooth.
Drizzle the melted white chocolate over the warm muffins (you can spoon it on or put it into a small bag and snip a corner to pipe). Serve.