Preheat the oven to 350 degrees C (180 degrees C). Line a muffin tray with muffin liners or spray it with baking spray.
Add butter and sugar to the bowl of a stand mixer fitted with a paddle attachment. Whisk the butter and sugar until light and fluffy. The color of the butter should become pale after whisking.
Scrape the sides of the bowl a few times while whisking. Add eggs, one at a time, and mix well after each addition.
Add vanilla extract, and buttermilk and mix well.
Now add bananas and mix well.
Add all-purpose flour, baking powder, baking soda, and salt to the bowl and mix just until combined.
Fold in the strawberries.
Use a large spoon (or an ice cream scoop) to transfer the batter to the muffin tray. Fill the cavity almost to the top.
Keep the muffin tray in the middle rack of the oven and bake for 18-20 minutes or until a toothpick inserted in the center of the muffins comes out clean.
Remove the tray from the oven and let the muffins rest in the tray for 5 minutes. Remove them from the tray and cool them on a cooling rack. Serve warm or at room temperature.