Mint Chocolate Cake

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Ingredients

1 cup (200g) granulated sugar
1/2 cup (8 Tbsp; 113g) unsalted butter, room temperature and cut into 8 pieces
1/4 cup (56g) extra-virgin olive oil
2 large eggs, at room temperature
1 Tablespoon (13g) pure vanilla extract or vanilla paste
1 cup (135g) all-purpose flour
1/2 cup (43g) unsweetened dutch-process or natural cocoa powder, sifted
1 teaspoon (5g) baking powder
1 teaspoon (5g) baking soda
1 teaspoon (6g) salt or fine sea salt
1/2 cup (120ml) hot water
2 cups (340g) dark chocolate, finely chopped* (see note)
1 and 1/4 cups (300ml) heavy cream or heavy whipping cream
1/4 teaspoon salt or fine sea salt*
2 teaspoons (8g) pure vanilla extract or vanilla paste
1/2 cup (8 Tbsp; 113g) unsalted butter, room temperature
1/2 cup (113g) vegetable shortening, room temperature*
2 Tablespoons (4g) fresh mint, finely chopped (plus more for garnish if desired)
3 and 1/2 cups (420g) confectioners’ sugar
2 teaspoons (8g) peppermint extract
3 Tablespoons (45ml) whole milk, room temperature

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