Blackberry Lavender Lemon Bars

Name: Blackberry Lavender Lemon Bars
Ingredients: ½ cup (1 stick) unsalted butter (at room temperature); ¼ cup granulated sugar; 1 cup all-purpose flour; 1 tablespoon cornstarch; pinch fine sea salt; 8 oz blackberries; 2 tablespoons granulated sugar; 2 teaspoons dried culinary lavender; 3/4 cup granulated sugar; 2 tablespoons all-purpose flour; 2 teaspoons finely grated lemon zest (from 1 large or 2 small lemons); ⅛ teaspoon baking powder; ¼ cup fresh lemon juice (from 2 juicy lemons); ½ teaspoon vanilla bean paste or extract; 2 large eggs (at room temperature); 1 large egg yolk (at room temperature); non-melting or powdered sugar (for topping)