Making the Blueberry Cake:

1. Preheat Oven: Set to 350°F. Grease and line three 8-inch cake pans with parchment paper.
2. Dry Ingredients: In a bowl, whisk together flour, baking powder, baking soda, and salt.
3. Cream Butter and Sugar: In a large bowl or mixer, beat butter, oil, and sugar for 2 minutes until fluffy.
4. Add Eggs: Mix in eggs one at a time, beating well after each. Scrape the bowl as needed.
5. Add Vanilla: Mix in vanilla extract.
6. Combine Buttermilk and Dry Ingredients: Alternately add buttermilk and flour mixture to the batter in thirds, mixing on low. Start and end with flour. Avoid over-mixing.
7. Layering: Spread about 1/2 to 1 cup of batter in each pan to cover the bottom, forming a 3/4-inch thick layer without blueberries.
8. Add Blueberries: Fold blueberries into the remaining batter, then divide it among the pans.
9. Bake: Bake for about 30 minutes, or until a toothpick comes out clean.
10. Cool: Let the cakes cool in pans for 10 minutes, then transfer to a cooling rack.

Making the Blueberry Jam:

1. Cook Blueberries: In a medium saucepan, cook blueberries, sugar, and lemon juice over medium heat for about 10 minutes.
2. Thicken Jam: Mix cornstarch with water, then stir into the blueberry mixture. Cook for 2 minutes until thick.
3. Cool Jam: Pour into a bowl, cover, and cool in the fridge.

Making the Blueberry Puree:

1. Blend Blueberries: Blend 1 cup of blueberries into a puree.
2. Reduce Puree: Cook puree in a saucepan over medium heat until reduced to 1/4 cup. Cool completely.
3. Making the Blueberry Cream Cheese Frosting:
4. Beat Butter and Cream Cheese: Beat butter and cream cheese for 30 seconds on medium speed.
5. Add Powdered Sugar: Gradually add half the powdered sugar, then beat on medium.
6. Add Blueberry Puree: Mix in blueberry puree.
7. Finish Frosting: Add remaining powdered sugar and beat for 1 minute. Adjust consistency if needed.

Assembling the Cake:

1. Start Layering: Place one cake layer on a plate. Spread a thin layer of frosting on top.
2. Pipe Frosting: Pipe a ring of frosting around the edge.
3. Add Jam: Fill the ring with blueberry jam.
4. Repeat: Place another cake layer on top and repeat the frosting and jam steps.
5. Top Layer: Add the final cake layer. Spread a thin layer of frosting on the top and sides for a crumb coat. Chill for 20-30 minutes.
6. Final Frosting: Apply the remaining frosting smoothly on top and sides.
7. Decorate: Garnish with fresh blueberries and mint leaves.