Mix warm water, brown sugar, and yeast in a large mixing bowl; stir well. Let stand until the yeast softens and begins to form a creamy foam, about 5 minutes. Grease a separate large bowl and set aside.
Stir whipped cream cheese, almond extract, milk, corn oil, honey, and salt into the yeast mixture. Transfer to a blender; blend until creamy and smooth.
Slowly stir all-purpose flour and cream cheese mixture together in a large bowl; add whole-wheat flour. Stir to make a smooth dough. Dough may be sticky, that's okay.
Grease a 8"x8" baking dish. Pour dough into this greased dish. Mix together topping ingredients and spread over entire top and sides of dough. Loosely Cover bowl with plastic wrap and let sit until double in size, about 1 hour in a warm place. I put mine in my oven with the light on for warmth. After dough has risen, remove from oven if that's where it was rising and preheat oven to 350 degrees F. Bake on center rack uncovered for about 55 minutes or until nicely browned and cooked through. Cool completely before slicing.