Prepare an 8x8-inch baking pan by lining it with parchment paper and lightly coating it with nonstick cooking spray. Set the pan aside.
In two separate medium bowls, place the white chocolate chips in one bowl and the semi-sweet chocolate chips in the other. Divide the sweetened condensed milk equally between both bowls, adding half to each.
Heat the semi-sweet chocolate and condensed milk mixture in the microwave, using 30-second intervals. Stir thoroughly after each interval until the chocolate is melted and smooth. Stir in 1 teaspoon of vanilla extract. Once combined, spread this mixture evenly across the prepared baking pan.
Next, melt the white chocolate and condensed milk mixture in the microwave, again using 30-second intervals and stirring after each until fully melted. Stir in the remaining teaspoon of vanilla extract, then fold in 1 tablespoon of Christmas sprinkles. Carefully spread this layer over the semi-sweet chocolate fudge in the baking pan.
Sprinkle the remaining Christmas sprinkles on top for a festive finish. Place the pan in the refrigerator and let it chill for at least 1 hour, allowing the fudge to set. Once firm, slice and serve.