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Preheat the oven to 375 degrees Fahrenheit. Line a 12-capacity muffin pan with muffin liners and grease the top of the pan.
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In a large bowl, mash the bananas together until they are completely blended into a paste. Set aside.
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In a medium-sized bowl, mix together the flour, baking soda, baking powder, nutmeg, and salt. Set aside.
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In the bowl of a stand mixer fitted with the paddle attachment, beat together the butter and sugar at medium speed until smooth. Add the eggs, one at a time, mixing well after each addition. Add the bananas and mix until smooth, then reduce the speed to low and add the flour mixture in 2 increments, mixing until *just* combined. Stir in the berries.
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To make the crumb topping, mix the sugar, flour and cinnamon together in a small bowl. Cut the butter into small pieces, roughly 1/2 inch in length and width, and put the pieces in the bowl as well. Then gently stir the mixture just enough to coat the butter pieces in the sugar mixture.
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Evenly distribute the batter between the muffin liners, filling them about 2/3 full. Sprinkle about 1 tablespoon of crumb topping over each muffin. Bake for about 20 to 30 minutes, or until a toothpick inserted into the center of each muffin comes out relatively clean, the tops of the muffins are golden brown, and the crumb topping has turned into a crust.