Preheat the oven to 375 degrees F. Grease a 12 cup muffin tin with cooking spray or butter.

In a medium sauce pot, combine the maple syrup, 1/4 cup brown sugar and 12 tablespoons butter. Cook over medium heat until the butter is melted and the sauce bubbling, about 8 minutes. Remove from the heat and stir in the vanilla.

Divide the pecans evenly among the bottom of 12 muffin cups. Now pour about 1-2 tablespoons of the sticky sauce over the pecans (reserve any remaining sauce for serving). The sticky sauce should come about 1/3 of the way up the muffin cup.

Add 6 tablespoons butter to saucepan. Allow the butter to brown lightly until it smells toasted, about 5 minutes. Stir often, butter will foam and then settle back down. Remove from the heat and let cool 10 minutes.

In a bowl, combine 2/3 cup brown sugar with the cinnamon.

Lightly flour a clean surface. Unfold 1 sheet of puff pastry with the folds going left to right. Brush the sheet with half of the brown butter and then evenly sprinkle with half of the cinnamon sugar. Repeat with the remaining sheet of puff pastry.

Starting with the end nearest you, roll the pastry up tightly like you would a cinnamon roll, finishing the roll with the seam side down. Cut about a 1/2-inch off the ends of each roll and discard. Slice each roll in 6 equal pieces, each about 1 1/2 inches wide. This should make 12 rolls. Place each roll, spiral side up, in the prepared muffin cups (place the rolls snugly into the pecans/sticky sauce).

Place the muffin pan on a cookie sheet with sides. Bake for 25-30 minutes until the sticky buns are golden to dark brown on top and firm to the touch. Allow to cool for 5 minutes only, invert the buns onto the parchment paper lined serving plate (ease the filling and pecans out onto the buns with a spoon). Rewarm the remaining sticky sauce and drizzle it over the buns. Sprinkle the buns with salt and serve warm.