To make the dough, heat milk in a small saucepan until 110-115 degrees. Transfer the milk to a measuring cup and stir in 1 tbsp. of sugar. Sprinkle yeast over milk and whisk to combine. Let sit for 5 minutes, or until yeast gets foamy. Add eggs and whisk until smooth. Combine the remaining 4 tbsp. of sugar in a bowl of a stand mixer fitted with a dough hook along with flour and salt. Add the milk mixture and with the mixer on, add the butter, 1 cube at a time. Mix on medium speed for 1 minute then knead on medium-high speed for 5 minutes.
Place dough in a (lightly greased bowl, using the 1/2 tbsp. of melted butter) and cover with a clean kitchen towel. Place in a warm, draft-free, area and let rise for 1 hour. After it has doubled in size, you're going to chill the dough for 2 hours.
In the meantime, preheat oven to 350 degrees and toast the pecans until fragrant, about 10-15 minutes. Set aside 1 1/4 cups of the chopped pecans for the buns.
Melt butter in a small saucepan then add dark brown sugar, cream, honey, and salt. Bring to a boil then reduce heat and simmer until glaze is a golden brown. Pour 1 cup of the glaze into a 8x8x2 baking pan. Tilt the pan back and forth to coat the entire bottom. Sprinkle the remaining 1/2 cup of chopped pecans over top of the glaze. Set pan aside.
For the filling for the buns, in a bowl of a stand mixer fitted with the paddle attachment, beat butter and brown sugar until light and fluffy. Add cinnamon, nutmeg, and salt.
When dough is ready, punch it down then transfer it to a lightly floured work surface. Roll out the dough into a 12x16" rectangle and about 1/4" thick. Spread the cinnamon sugar mixture onto the dough with an offset spatula, leaving a 1" border around the edges.
Sprinkle 3/4 cups of the chopped pecans on top of the cinnamon sugar mixture.
Beginning with the longest edge closest to you, start rolling the dough into a log, tightening as you roll. Pinch together the ends to seal. Arrange the log seam side down.
Using floss or a sharp knife, cut the log into 9 equal pieces. Turn the bun cut side up and reshapen, if need be.
Place the buns, cut side up, in the prepared pan, spacing them evenly apart. Cover with a clean kitchen towel and let rise for 45 minutes - 1 hour in a warm, draft-free area.
Preheat oven to 350 degrees and whisk an egg in a small bowl. Using a pastry brush, brush the tops of the buns with the egg wash.
Bake buns for 50 minutes, or until golden brown and bubbly. If they're browning too quickly, you can tent them with foil.
Serve buns warm or at room temperature.