Lemon Raspberry Cake

Name: Lemon Raspberry Cake
Ingredients: Baking spray with flour, for the pans (optional); 2 1/2 c. all-purpose flour; 2 tsp. baking powder; 1/4 tsp. baking soda; 1/4 tsp. kosher salt; 1 3/4 c. granulated sugar; 8 tbsp. (1 stick) salted butter, melted and cooled slightly; 1/2 c. vegetable oil; 2 tbsp. lemon zest plus 1/3 c. fresh lemon juice (from 2 to 3 lemons); 3 large eggs, at room temperature; 3/4 c. buttermilk, at room temperature; 2 tsp. vanilla extract; 1 tbsp. cornstarch; 3/4 c. seedless raspberry jam; 1 c. (2 sticks) salted butter, at room temperature; 1/3 c. seedless raspberry jam; 1 tbsp. fresh lemon juice; 1 tsp. vanilla extract; 5 c. powdered sugar; 1 (6-oz.) container raspberries (optional)