Mix flour, brown sugar, baking powder, cinnamon, baking soda, salt, ground ginger, and ground cloves together in a bowl.
Cut unsalted butter chunks into flour mixture with a pastry blender until mixture resembles coarse crumbs; make a well in the center.
Pour pumpkin puree, yogurt, and 1 teaspoon vanilla extract into the well in flour mixture; stir with a wooden spoon until a soft dough forms.
Mix pecans into dough.
Turn dough out onto a lightly floured surface and pat into two equal-size circles.
Cut each circle into 8 wedges; transfer to a baking stone or baking sheet lined with parchment paper.
Bake scones in the preheated oven until firm to the touch and lightly browned, 12 to 15 minutes.
Heat butter in a skillet over medium heat until butter is foaming and nut-brown in color, 3 to 5 minutes.
Beat brown butter, confectioners' sugar, milk, and 1/2 teaspoon vanilla with an electric mixer on medium-high speed until sugar is dissolved and glaze is shiny, 3 to 4 minutes, adding more milk as necessary.