Blackberry Cake

Ingredients:

8 ounces (227 g) buttermilk (or regular milk with 1 Tbsp white vinegar added) (Make sure your buttermilk is fairly fresh, the older buttermilk is the higher the acidity level)
3 ounces (85 g) of vegetable oil
3 large eggs
1 tablespoon lime zest (About 1 lime)
1 tablespoon lime juice
12 ounces (340 g) of all-purpose flour
11 ounces (312 g) of granulated sugar
1 teaspoon salt
1 teaspoon baking soda
8 ounces (227 g) of unsalted butter
2 tablespoons all-purpose flour (For dusting on blackberries)
4 ounces (113 g) of blackberries (You can use frozen, but don’t thaw them)
Blackberry Puree:
16 ounces (453 g) of fresh or frozen blackberries
1 tablespoon lime zest
2 tablespoon lime juice
1 tablespoon corn starch
1/8 teaspoon salt
Blackberry Buttercream Frosting:
24 ounces (680 g) unsalted butter at room temperature (You can use salted butter but it will affect the taste and you need to leave out additional salt)
24 ounces (680 g) powdered sugar sifted if not from a bag
2 teaspoons vanilla extract
6 ounces (170 g) of pasteurized egg whites at room temperature
2 ounces (57 g) blackberry puree (You can add more if you want to)
1 drop Americolor electric pink food coloring (Optional)