Preheat the Oven:**
- Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans or line them with parchment paper.
**Prepare the Chocolate Cake:**
- In a large mixing bowl, sift together the flour, sugar, cocoa powder, baking powder, baking soda, and salt.
- Add the milk, vegetable oil, eggs, and vanilla extract to the dry ingredients. Beat on medium speed for about 2 minutes, until well combined.
- Gradually add the boiling water to the batter, mixing on low speed until smooth. The batter will be thin, but this is normal.
- Pour the batter evenly into the prepared cake pans.
- Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
- Allow the cakes to cool in the pans for 10 minutes, then turn them out onto a wire rack to cool completely.
**Prepare the Peanut Butter Filling:**
- In a medium bowl, beat the peanut butter and softened butter together until smooth and creamy.
- Gradually add the powdered sugar and vanilla extract, beating until fully incorporated.
- Add the milk, one tablespoon at a time, until the filling reaches a smooth, spreadable consistency.
**Prepare the Chocolate Ganache:**
- Place the chopped chocolate in a heatproof bowl.
- In a small saucepan, heat the heavy cream over medium heat until it begins to simmer (do not let it boil).
- Pour the hot cream over the chopped chocolate and let it sit for 2-3 minutes to melt.
- Add the butter and stir until the mixture is smooth and glossy. Let the ganache cool slightly until it thickens but is still pourable.
**Assemble the Cake:**
- Once the cakes are completely cooled, place one layer on a serving plate or cake stand.
- Spread the peanut butter filling evenly over the top of the first layer.
- Place the second cake layer on top.
- Pour the chocolate ganache over the top of the cake, letting it drip down the sides. Use a spatula to spread the ganache evenly over the cake.
**Serve:**
- Let the cake sit for at least 30 minutes to allow the ganache to set.
- Slice and serve the cake at room temperature. Store any leftovers in an airtight container.