Combine the raspberry filling ingredients in a medium saucepan. In a bowl, mix frozen raspberries with 1/4 cup sugar and 1 tbsp cornstarch, adding 2 tbsp water or lemon juice. Over medium heat, stir occasionally until the mixture thickens like jam, about 8-10 minutes. Pour into a dish and refrigerate to cool.

Mix the cream cheese layer. In a medium bowl, thoroughly mash 12 oz cream cheese with 1/3 cup sugar using a fork. Add 1 tsp vanilla extract and 1 large egg. Switch to a whisk and blend until nice and creamy, then set aside.

Preheat your oven to 350°F (175°C). Meanwhile, grease a 9×13 baking dish and line the bottom and two longest sides with parchment paper for easy removal.

Whisk the dry ingredients for the crumble base in a large bowl. Combine 1/2 cup light brown sugar, another 1/2 cup granulated sugar, 2 3/4 cups flour, 1/2 tsp salt, and 1 tsp baking powder. Break up any lumps in the brown sugar as you mix.

Incorporate the melted butter. Stir in 1 cup of cooled, melted unsalted butter with a silicone spatula until the mixture is crumbly and well combined.

Assemble the bars. Press about ⅔ of the crumble mixture into the bottom of the pan to form a thin layer. Spread the cream cheese mixture evenly on top, then add the cooled raspberry filling, spreading carefully. Sprinkle the remaining crumble over the top.

Bake for 35 to 40 minutes. Look for golden edges and a surface that appears dry. The center should jiggle slightly when nudged. Allow the bars to cool for 20 minutes at room temperature, then chill in the refrigerator for about 2 hours until firm. Once chilled, lift out and slice into 12 squares.