Preheat oven at 350-degrees. Line an 8x8 or 9x9 pan with heavy foil and apply butter or nonstick spray.
Beat together cream cheese, 1/4 cup sugar, and 1 egg until fairly smooth; some small chunks are fine. Stir in 1 cup chocolate chips.
In a microwave safe bowl, heat the butter and remaining 1 cup chocolate chips in brief bursts until fully melted and smooth; watch it carefully and stir well between each burst. Stir in the remaining 1/2 cup sugar, followed by the 2 eggs, flour, baking powder, and salt.
Pour half the chocolate batter into the ready pan and spread into an even layer. Gently spread the cream cheese batter on top. Drop dollops of the rest of the chocolate batter on top. Use a butter knife or narrow spatula to swirl the layers together for a marbled effect.
Bake until the top is crinkled and edges are pulling away from the sides of the pan, about 25 to 30 minutes. Let cool at room temperature for an hour, then stash in the fridge for another few hours to completely cool.
Use the foil to lift the contents onto a cutting board to slice into bars. Store in a sealed container in fridge, waxed paper between stacked layers to prevent stocking, for up to three days, or freeze for later enjoyment.
OM NOM NOM!