Position a rack in the center of the oven and preheat the oven to 350 F. Line a standard muffin pan with liners or spray well with cooking spray.
Place the bananas (peel on) on a baking sheet and roast for 12 to 15 minutes, or until the skins are completely black and glossy. Remove from the oven, allow to cool slightly, then peel and mash the bananas, including any liquid released. Set aside.
In a medium bowl, whisk together the flour, baking soda, salt, and cinnamon. Set aside these dry ingredients.
In a small saucepan set over medium heat, melt the butter. Continue cooking, giving it a swirl occasionally, until the butter foams, then turns golden brown and smells nice and nutty. Remove from heat and allow it to cool until no longer hot but still liquid.
In the bowl of a stand mixer with the paddle attachment, combine the browned butter and sugar. Beat on medium speed until combined and slightly thickened, 2 to 3 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary.
Reduce the mixer to low and add the eggs, one at a time, adding the next egg only after the previous one has been fully incorporated, scraping down the bottom and sides of the bowl after each addition.
Add the sour cream and vanilla bean paste all at once and beat on low until combined. Gradually add the dry ingredients and beat until just combined.
Add the mashed bananas and mix on low until evenly distributed throughout the batter. Scrape down the bottom and sides of the bowl once more, and mix briefly to ensure everything is incorporated.
Divide the batter evenly among the prepared muffin cups, filling each about 3/4 full. Sprinkle the tops generously with turbinado sugar, gently pressing it into the batter.
Bake for 18 to 24 minutes, or until a skewer inserted into the center of a muffin comes out with a few moist crumbs attached.
Cool the muffins in the pan for 5 minutes, then transfer to a wire rack to cool completely. Serve warm or at room temperature. Store tightly covered at room temperature for up to 3 days.