Preheat your oven to 350°F (175°C). Grease your 9x13-inch baking pan with a little butter or cooking spray to ensure easy removal later.
In a large mixing bowl, combine the cake mix, melted butter, and egg. Mix until well combined and a thick batter forms.
Pour the batter into the prepared baking pan. Use a spatula to spread it evenly across the bottom of the pan.
Gently fold the raspberries into the condensed milk in a separate bowl. Spoon the raspberry mixture over the batter in the pan, spreading it out evenly.
In a small bowl, mix together the brown sugar, flour, cold butter pieces, and cinnamon. Blend until you have a crumbly topping. Sprinkle this mixture over the raspberry layer.
Sprinkle the white chocolate chips evenly over the top of the crumbly mixture.
Place the pan in the preheated oven and bake for about 30-35 minutes, or until the top is lightly golden and a toothpick comes out clean.
Allow the Gooey Raspberry Coffee Cake Bars to cool in the pan for at least 10 minutes before slicing them into squares.