Brown the Ghee. Measure 103 grams (1/2 cup) of ghee using a kitchen scale. Melt the ghee on the stove over medium-low heat until it turns a light golden brown. Since ghee is already clarified butter, it will not brown as deeply as regular butter, so keep a close eye on it to avoid burning.
Combine the Wet Ingredients. In a large mixing bowl, combine the mashed bananas, jaggery, yogurt, and vanilla extract. Whisk the mixture thoroughly until the ingredients are well combined, and the jaggery has begun to incorporate into the base. Slowly pour the melted, browned ghee into the wet ingredients, whisking constantly as you go. Continue to whisk well until the ghee is fully emulsified. and the mixture is smooth and uniform.
Mix in Dry Ingredients. Add the all-purpose flour, whole wheat flour, sooji (semolina), baking soda, baking powder, cardamom powder, and salt. Using a spoon, mix the batter just until combined - be careful not to overmix to ensure a tender crumb.
Bake. Transfer the batter into a greased 11" x 5" loaf pan. Bake at 350 degrees for 45 minutes, but start checking at the 40-minute mark. Once done, let the banana bread cool in the pan for 10 minutes before slicing. Enjoy warm!