Put the vegetable oil, buttermilk, eggs, granulated sugar, brown sugar, and vanilla in a bowl. Whisk until combined.
In a separate bowl, combine the flour, baking powder, ground cinnamon, baking soda, salt, and ground allspice. Add to the wet ingredients and stir until combined. Set aside for 15-20 minutes.
While waiting, preheat the oven to 425˚F and line a 12-count muffin pan with cupcake liners. Then, prepare the crumb topping by combining the flour, brown sugar, and ground cinnamon. Stir in the melted butter until crumbly and set aside.
Fold the diced peaches into the muffin batter.
Fill the lined muffin cups with batter. Crumble the crumble topping over the batter and gently press it into the batter to help it stick.
Bake at 425˚F for 6 minutes. Then, leaving the pan in the oven, turn it down to 350˚F and continue baking the muffins for 15-18 minutes or until a toothpick inserted in the center comes out clean.
Cool in pan for 10 minutes. Remove from pan and cool completely on wire rack.
Whisk the powdered sugar, whole milk, and vanilla until smooth. Drizzle over the cooled muffins.
Video
Notes
Line an airtight container with paper towels before adding the cooled muffins. Store them at room temperature for 1-2 days, in the fridge for 3-4 days, or in the freezer for 2-3 months.