Make the cookies. In a large mixing bowl with a hand mixer or in a stand mixer fitted with the paddle attachment, cream butter, brown sugar and salt on medium speed until light and fluffy, about 3 minutes.
Beat in egg yolks and vanilla just until combined.
Add the flour and pecans to the creamed mixture and beat just until the remaining streaks of flour disappear, ensuring to scrape the bowl.
Divide the dough in half and place each half on a long sheet of plastic wrap. Shape both halves into 12-inch rolls. Wrap each tightly in the plastic wrap. Refrigerate for 1 to 2 hours until firm.
Preheat the oven to 350°F and set two oven racks to divide the oven into thirds. Line two half-sheet trays with parchment paper or silicone mats. Unwrap and cut one log into 1/4-inch slices. Place 20 cookies, about an inch apart, on each sheet.
Bake for 11 to 13 minutes or until golden brown, switching the tray’s places in the oven and rotating them front to back halfway through.
Allow cookies to cool on their trays for 2 to 3 minutes then transfer to wire racks to cool completely.
Make the filling. In a saucepan, melt the butter over medium-low heat. Cook the butter, stirring and scraping the bottom occasionally, until it begins to bubble and pop. Continue cooking until the butter foams and you can see brown flecks swimming in the butter when you stir. You’ll know it’s done browning when you no longer hear bubbling and popping — as that’s when all the water has been cooked off.
Remove butter from the heat and add powdered sugar, vanilla and two tablespoons of cream. Stir until smooth. Add the remaining cream if needed to achieve a spreading consistency.
Spread or pipe on the bottoms of half of the cookies. Top with remaining cookies.