Preheat the oven to 350°F and line a 9x5" loaf pan with parchment paper. Set aside.

In a large mixing bowl, mash the bananas until mostly smooth. A few small lumps are fine. You can use a fork, potato masher, or even a whisk if your bananas are very soft.

Add the granulated sugar, brown sugar, and oil to the mashed bananas and whisk until fully combined. Mix in the eggs, vanilla extract, and vinegar, whisking until the mixture is smooth and cohesive.

Add the flour, baking powder, baking soda, salt, and cinnamon. Gently fold the dry ingredients into the wet ingredients using a rubber spatula. When a few streaks of flour are still visible, fold in the chopped strawberries and continue mixing just until the batter comes together and no dry spots remain. Be careful not to overmix.

Pour the batter into the prepared pan and smooth the top. Bake at 350°F for 55-65 minutes, or until a toothpick or knife inserted into the center comes out clean with just a few moist crumbs attached. If the top is browning too quickly, loosely tent the loaf with foil for the remaining bake time.

Let the bread cool in the pan for about 10 minutes, then carefully lift it out and transfer to a wire rack to cool completely before frosting.

Beat the room temperature cream cheese and butter together on medium-high speed until smooth and creamy.

Add the jam and vanilla and mix until combined.

Reduce the speed to low and gradually mix in the powdered sugar, scraping down the bowl as needed, until smooth. Mix in a tiny drop of red food coloring for a soft pink color if desired.

Once the bread is completely cool, spread the frosting evenly over the top. Slice and serve.