In a bread machine, add the following ingredients in the order suggested by your manufacturer: 6 tablespoons of sliced butter, flour, eggs, milk, salt, sugar, and yeast. Process on the dough cycle.
When the dough cycle is done, roll the dough into a 20 by 12 rectangle. Paint the dough with the melted butter and sprinkle on the cinnamon and 2/3 cup packed brown sugar. Roll up the twenty inch side, and then cut it into 12 equal slices. Place them in a greased (with butter) non-stick metal 13 by 9 baking dish. Cover and let rise for 30 minutes in a warm place.
Meanwhile, preheat the oven to 375 degrees. Toast the pecans in a skillet on medium heat, until they're slightly toasted.
Bake the buns for twenty minutes. Make the glaze by melting together the six tablespoons of butter, the ⅔ cup packed brown sugar, the cream, and the corn syrup. Then add the pecans and vanilla and set the pot aside.
Remove the buns from the pan immediately, and pour the warm glaze over the buns.