Place 1/2 tablespoon of butter in a coffee mug and microwave for 5 seconds to soften. Stir in the sugar, honey, applesauce, and vanilla until well-mixed.
Add 1/4 cup of flour, baking powder, and salt, and stir until just combined.
Gently fold in the mixed berries. In a small bowl, combine the remaining flour with the brown sugar and cinnamon.
Cut in the remaining butter until coarse crumbs form. Pour streusel topping over cake batter.
Warm cake in microwave for 1 to 1 1/2 minutes, or until a toothpick inserted in the center of the cake comes out clean.