How to Make It
Prepare the Cake: Preheat oven to 350°F. Grease and flour a 13- x 9-inch cake pan, and line bottom with parchment paper; lightly grease parchment paper.
Whisk together sugar, baking powder, baking soda, salt, cardamom, and 2 1/2 cups of the flour in a large bowl. Whisk together buttermilk, tahini, water, butter, vanilla, and eggs in a medium bowl. Whisk buttermilk mixture into flour mixture until thoroughly combined. Toss blueberries with remaining 1 tablespoon flour; gently fold coated blueberries into batter.
Spoon batter into prepared pan. Bake in preheated oven until a wooden pick inserted in center comes out clean, 40 to 45 minutes. Cool in pan on wire rack for 20 minutes. Invert on wire rack and cool completely, about 1 hour.
Prepare the Strawberry Buttercream: Beat butter with a heavy-duty stand mixer on medium speed until creamy. Gradually add powdered sugar, vanilla extract, salt, and 2 tablespoons of the milk, beating until blended. Gently fold in chopped strawberries. Stir in remaining 1 tablespoon milk, 1 teaspoon at a time, until desired consistency is reached. Frost cake with Strawberry Buttercream.