Set aside 1/2 cup of raspberries. In a small saucepan over medium heat, combine the remaining 1 cup of raspberries with 2 tablespoons of sugar, the lemon juice and the cornstarch. Bring to a boil, stirring occasionally. Boil for 1 minute, then turn the heat down to low and simmer until thickened to a jam consistency, about 4-6 minutes. Stir in the reserved raspberries. Transfer the mixture to a bowl and set aside to cool to room temperature.

Preheat the oven to 350ºF (180ºC). Line two large cookie sheets with parchment paper.

In a medium bowl, whisk together the all purpose flour, the cake flour, salt and baking soda until well combined.

In a large bowl, beat the butter, the remains 3/4 cup of sugar, and the brown sugar, with an electric mixer at medium speed, until light and fluffy. Beat in the egg and the egg yolk in two separate additions until well incorporated. Beat in the extracts.

Mix the flour mixture into the batter, just until combined. Stir in the white chocolate pieces. Fold in the cooled raspberry mixture very gently. Do not over mix! You want to see raspberry swirls. Over mixing will change the texture of the cookies.

Place 2-tablespoon size portions of cookie dough about 3 inches apart onto the prepare cookie sheets. I used a #30 portion scoop.* Top each cookie with a piece of white chocolate and sprinkle with coarse sugar. Bake until the tops of the cookies are set and the edges turn light golden brown, about 10-14 minutes. Transfer to a cooling rack.