Preheat oven to 400 degrees F. Lightly grease a 12-cup muffin tin and set aside. Remove puff pastry from freezer and let sit out on the counter to thaw for 15 minutes.
In a bowl combine the 1.5 sticks of softened unsalted butter and brown sugar. Stir together until well mixed.
Spoon the butter and sugar mixture into the muffin tin distributing it evenly between the 12 cups.
Divide 1 cup of chopped pecans between the 12 cups.
Place 1 sheet of the thawed puff pastry dough on a floured surface and lightly roll it with a rolling pin to very slightly flatten it. This should not increase the size of the sheet by much but will help flatten the creases a bit.
Spoon 1 tablespoon of butter onto the puff pastry and use the back of the spoon to spread it over the dough leaving about a ½ inch boarder around the edges.
In a small bowl combine the remaining ⅔ cup brown sugar and 3 teaspoons of cinnamon and mix well before sprinkling half of it over the buttered pastry dough.
Sprinkle ½ cup of chopped pecans over the cinnamon sugar.
With the puff pastry in front of you with the longest side facing you roll the pastry up finishing with the seam-side down.
Trim the ends of the roll about ½ inch and discard the ends. Then slice the roll into 6 equal slices.
Place each slice in a muffin cup with the spiral facing up. This will fill 6 muffin cups.
Repeat steps 1-11 with the second puff pastry sheet.
Once all 12 muffin tin cups are filled place the pan in the oven and bake for 25-30 minutes or until the dough is golden brown on top.
Remove from the oven and let cool for 5 minutes. Place a piece of parchment paper or a clean cutting board on the counter and carefully turn the muffin pan over onto the flat surface gently removing each sticky bun. If any of the sticky pecan mixture remains in the pan use a spoon the gently remove it and place it on top of the buns. Note: do not wait longer than 5 minutes or the buns may get stuck in the muffin pan.
Let buns cool for at least 30 minutes before serving.