Line bottom and sides of a 9-inch springform pan with parchment paper.
In a medium saucepan, melt butter over medium heat. Cook until butter turns a medium-brown color and has a nutty aroma, about 10 minutes. Remove from heat, and transfer to a small bowl.
In the bowl of a stand mixer fitted with the paddle attachment, combine 1½ cups (188 grams) flour, 2 tablespoons (24 grams) sugar, yeast, and 1½ teaspoons (4.5 grams) salt.
In a medium saucepan, heat milk, ⅓ cup (80 grams) water, and ¼ cup (60 grams) browned butter over medium heat until an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add warm milk mixture to flour mixture, and beat at medium speed until combined. Add egg, beating until combined. With mixer on low speed, gradually add remaining 1¼ cups (156 grams) flour, beating just until a shaggy dough forms.
Switch to the dough hook attachment. Beat at low speed until a soft, somewhat sticky dough forms, 6 to 7 minutes, stopping to scrape sides of bowl and dough hook. Cover and let stand in a warm, draft-free place (75°F/24°C) for 10 minutes. (Dough will puff slightly.)
In a medium bowl, stir together ground pecans, remaining ⅓ cup (67 grams) sugar, and remaining ¾ teaspoon (2.25 grams) salt.
Turn out dough onto a lightly floured surface. (Do not punch down.) Gently divide dough into 14 portions (about 45 grams each). Dip each portion in remaining browned butter, and roll in pecan mixture. Arrange evenly in prepared pan. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 30 to 40 minutes.
Preheat oven to 350°F (180°C).
Sprinkle top of dough with any remaining pecan mixture.
Bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 25 to 30 minutes. Let cool in pan for 10 minutes. Remove from pan, and discard parchment paper. Serve warm or at room temperature with Vanilla Dipping Sauce.