For cream cheese filling, combine cream cheese and sugar in a mixing bowl and beat with an electric mixer until smooth. Add egg, lemon juice, and vanilla and continue beating until well mixed. Use a spatula to fold in hazelnuts. Cover and refrigerate.
For brownie batter, melt chocolate morsels and butter in the top of a double boiler over simmering water over medium heat. Remove from heat and set aside.
Sift together flour, cocoa, baking powder, and salt in a medium bowl and set aside.
Preheat oven to 350°. Combine sugar, eggs, and vanilla in a large mixing bowl and beat with an electric mixer until smooth and lemon-colored, about 2 minutes. Beat in melted-chocolate mixture, then add flour mixture and continue beating until mixture is smooth. Fold in hazelnuts with a spatula.
Spread half the chocolate batter into an 8" square baking pan. Spread cream cheese filling over chocolate. Gently spread remaining brownie batter over cream cheese layer. Pull a spatula through layers to create a marbleized effect. Bake for about 40 minutes. Allow to cool before cutting into 2" squares.