Preheat the oven to 335º F/168º C or 350º F/177º C and prepare three 6-inch cake pans (or two 8-inch pans) with cake goop or another preferred pan spray or parchment paper. Make sure all ingredients are at room temperature or slightly warm (eggs, buttermilk, butter). Measure out the buttermilk and place 4 ounces in a separate measuring cup.
Add oil to the 4 ounces of buttermilk and set aside.
To the remaining buttermilk, add your eggs (lightly whisked to break them up), lemon extract, lemon juice, and lemon zest.
Measure out the cake flour, sugar, salt, baking powder, and baking soda into the bowl of your stand mixer.
Attach the paddle to the mixer and mix on low speed (setting 1 on Kitchen Aid mixers) until the dry ingredients are combined. I recommend a stand mixer for this recipe, but you can do this with a large bowl and electric mixer, just mix by texture instead of time.
Slowly add chunks of softened butter to the flour mixture and mix on medium speed until the batter resembles coarse sand.
Add the milk/oil mixture all at once to the dry ingredients and mix on medium speed (speed 4 on Kitchenaid) for 2 full minutes until it's white and fluffy.
Scrape the bowl. This is an important step because if you skip it, you will have hard lumps of flour in your batter. If you do it later, they will not mix in fully.
Slowly add in the rest of your wet ingredients in 3 parts and mix until combined. Stop to scrape the sides of the bowl one more time halfway through. Your batter should be thick and not too runny.
Fill the pans ¾ full and give each a tap to level out the batter and get rid of any air bubbles.
Add 3 to 4 large dollops of your raspberry filling to the cake batter and use a spoon or knife to swirl it through the batter.
Bake the cakes for 35 to 40 minutes until a toothpick inserted in the center comes out with a few crumbs.
After the cakes have cooled for 10 minutes, flip them onto cooling racks to cool completely. Or wrap them in plastic wrap and freeze them.