Chef John's Sticky Buns
1 cup chopped toasted pecans 1 large egg, beaten 1 pinch salt 1 teaspoon ground cinnamon 1 ½ teaspoons fine salt 2 tablespoons white sugar 2 teaspoons active dry yeast 3 tablespoons water 4 cups all-purpose flour, or more as needed 6 tablespoons unsalted butter, melted ¼ cup white sugar ½ cup packed light brown sugar ¾ cup packed light brown sugar ⅔ cup warm milk ⅔ cup warm water