Preheat the oven to 300 degrees. Grease an 8-inch cake pan with the 1 tablespoon butter. On a cookie sheet, toast the pecans for 8 minutes. Turn the pan once for even toasting. In a bowl, combine the Graham cracker crumbs, sugar, butter and pecans. Pat evenly over the bottom of the pan.
In a small saucepan, simmer the port and dried blueberries for 3 minutes. set aside to cool. Put the cream cheese, butter, sugar and cornstarch in a mixing bowl and beat on medium, just to blend. Add eggs, 1 at a time, then sour cream, vanilla and blueberry mixture. Pour batter into prepared pan. Set into hot water bath and bake for 1 hour and 15 minutes, and slightly puffed and firm. Cool on rack. Refrigerate, then remove from pan.
In saucepan, simmer 3/4 cup port and sugar for 3 minutes. Meanwhile whisk together cornstarch, vanilla and remaining 1/4 cup of port. Add slurry to pan and simmer for 2 more minutes. Add half of blueberries and cook until berries burst and sauce thickens. Remove from heat and let cool. Stir in remaining berries.