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Heat oven to 335°F. Grease and line three 8-inch pans.
Stir milk and vinegar together; rest 5 minutes.
Whisk banana, yogurt, oil, sugars, and vanilla. Stir in milk mixture.
Whisk remaining dry ingredients together.
Fold dry ingredients into wet ingredients just until smooth.
Divide batter evenly among pans. Bake 28–32 minutes until set.
Rest cakes 15 minutes, then wrap warm and chill.
For filling: Melt butter. Stir in sugar and cinnamon; cook until glossy.
Whisk in cream; simmer 1–2 minutes.
Remove from heat; add salt and vanilla. Cool completely.
Once cold, whisk in milk as needed until spreadable.
For frosting: Beat butter and cream cheese until smooth. Add powdered sugar gradually.
Mix in vanilla and salt. Add milk as needed. Whip until fluffy and pipeable.
Pipe thin frosting dam on each cake layer.
Spread thin frosting inside dam.
Spoon one-third of filling over each layer.
Stack layers and chill briefly.
Frost exterior of cake.
Optional: Drizzle or swirl filling on top.