Steps
1. In a small bowl, combine warm milk, yeast, and a pinch of sugar; let it activate for 5 minutes until foamy.
2. In a mixing bowl, whisk together flour, sugar, and salt.
3. Add the activated yeast mixture, melted butter, and egg yolk to the dry ingredients; mix until a sticky dough forms.
4. Cover the dough and let it rest in a warm place for 1 hour, until it doubles in size.
5. On a floured surface, roll out the dough to about 1/4 inch thickness and cut into 2-inch squares.
6. Heat vegetable oil in a deep pan to 350°F (175°C).
7. Fry beignets in batches until golden and puffed, about 2 minutes per side; drain on paper towels and dust with powdered sugar if desired.
8. To make the pecan pie sauce, melt butter in a small saucepan over medium heat.
9. Stir in brown sugar and cook until it dissolves and the mixture is bubbly.
10. Carefully whisk in heavy cream, vanilla extract, and salt; simmer for 2 minutes until thickened.
11. Remove from heat and stir in chopped pecans.
12. Serve warm beignets with the pecan pie dipping sauce on the side.