In a small pot, combine the raspberries, sugar, and lemon juice. Heat over medium low until the raspberries burst and thicken, around 20-30 minutes. Remove from heat, then press mixture through a sieve to remove seeds. Set aside.
Preheat the oven to 350 degrees. Lightly grease a 10-inch cast iron skillet or round baking pan with non-stick spray, then set aside.
For The Brownie
In a medium-sized bowl, whisk the melted butter and sugars together until the sugar has dissolved. Add the cocoa powder, whisking until dissolved and smooth. Beat in the egg and vanilla until well incorporated, then stir in the flour and salt until the batter is smooth and thick. Set aside.
For The Cookie Dough
In a separate medium-sized bowl, beat the butter and sugars together until light and fluffy, around 3 minutes. Add the egg and vanilla, beating until smooth. Add in the flour, baking soda and salt, stir in the dry ingredients until a cookie dough forms. Fold in half of the chocolate chips, then set aside.
Pour the brownie batter into the skillet and spread out evenly with a spatula. Swirl the raspberry sauce throughout the brownie with a spoon. Scoop the cookie dough into the brownie batter, then sprinkle with the remaining chocolate chips.
Bake for 25-30 minutes, or until the cookie is golden and the edges are set and pulling away from the sides of the pan. Do not over-bake.
Allow to cool in the pan for about 10 minutes and serve hot with your favorite flavor of ice cream.
The raspberry sauce can be prepared in advance and stored in the fridge for up to three days prior.