1. Preheat oven to 350 degrees. Butter and flour a 14-cup nonstick Bundt pan. Whisk together 3 cups flour, baking soda, and salt. Toss peaches with remaining 2 tablespoons flour to coat. In a large bowl, using a mixer, beat 2 sticks butter and 2 cups sugar on medium-high until fluffy and pale yellow. Beat in eggs, one at a time, until incorporated. With mixer on low, add flour mixture in 2 additions, alternating with sour cream, and beat until combined. Fold peaches and vanilla into batter and transfer to pan. Tap pan firmly on counter several times to remove any air bubbles and smooth top.

2. Bake until a toothpick inserted in center comes out clean, 1 hour. Transfer pan to a wire rack set over a rimmed baking sheet; let cool 15 minutes.

3. Meanwhile, melt remaining 1 stick butter. Combine remaining 1/4 cup sugar and cinnamon. Using an offset spatula or small knife, loosen cake from pan, then invert onto rack. Working in sections, brush cake with butter and sprinkle liberally with cinnamon sugar. Serve warm or at room temperature, with whipped cream if desired.