In a food processor or blender, add the eggs, milk, oil, vanilla, bananas, sugar, salt, and flour. Blend until the batter is smooth without clumps.
In a medium nonstick skillet over medium heat, melt the butter and swirl so it coats the entire pan. Then pour in ¼ cup of crepe batter and tilt the pan to cover the entire bottom. Cook until the bottom surface of the crepe begins to brown and the edges are lacey, for about 3 minutes, and then flip. Repeat with the remaining crepe batter.
In a food processor or blender, add the strawberries and puree until smooth. Pour the strawberry puree through a sieve into a medium bowl to remove any seeds and clumps. Chill for 15 minutes until the puree is cold.
In a large bowl, using a whisk or hand mixer, beat the cream until thickened. Add the powdered sugar, and beat until soft peaks form. Add half of the strawberry puree, and blend with the hand mixer. Add the rest of the strawberry puree and gently fold it into the whipped cream with a spatula.
Dollop a bit of strawberry cream on a plate, then place the first crepe and frost with about ¼ cup of filling. Stack the remaining crepes on top of each other, with strawberry whipped cream between each layer. Spread the rest of the strawberry whipped cream on top of the last crepe.