Line a quarter sheet pan with parchment, leaving a 1 inch overhang.
Heat 8 tablespoons butter in a skillet over medium heat until melted, about 2 minutes. The butter will bubble and splatter, continue cooking, swirling or stirring with a rubber spatula, until butter starts to turn golden, 2–4 minutes. Turn off heat and continue cooking over warm (but off!) burner until deeply golden and has a nutty aroma, about 1 more minute.
Immediately pour butter into prepared sheet pan, scraping to get all browned milk solids; freeze until solid, about 45 minutes.
Grind 2 cups (88g) freeze dried bananas into a powder in a food processor. Measure out 1 tablespoon (7g) for the topping, cover and set aside.
In a mixing bowl, combine remaining ground banana (81g), 1½ cups (187 g) all-purpose flour, ⅓ cup (67g) sugar, 1 tablespoon (14g) baking powder, ½ teaspoon salt, ½ teaspoon cinnamon, and ½ teaspoon ginger.
Remove browned butter from freezer, peel off parchment, then chop and add to flour. Using a pastry blender, cut butter into flour until pea-sized. Stir in ½ cup (55g) pecans.
In a liquid measuring cup, stir together ¾ cup (173g) buttermilk and ¾ teaspoon vanilla bean paste. Form a well in center of flour butter-mixture; buttermilk mixture in and, using a rubber spatula, mix until a dough comes together.
Transfer dough to a piece of parchment and lightly press / fold into a 8✕5-inch rectangle (about 1-inch thick); transfer to fridge until edges are firm, about 1 hour.
Meanwhile, heat oven to 400ºF (204ºC) with rack set in middle position.
Melt remaining 2 tablespoons butter in a heatproof bowl in the microwave. Combine reserved 1 tablespoon ground bananas and 1 tablespoon granulated sugar for topping.
Cut biscuit dough in half lengthwise then cut each half into 4 squares. Flip the dough over, peel off parchment, then transfer scones to a parchment lined backing sheet.
Brush biscuits with melted butter then sprinkle with banana-sugar topping.
Bake until risen and golden brown on tops and sides, 15-17 minutes, rotating halfway through. Let cool on sheet 5 minutes. Then transfer to a cooling rack.