Preheat oven to 350°F and spray an 8½ x 4½-inch loaf pan with nonstick cooking spray.

In the bowl of a stand mixer with the paddle attachment, add eggs, sugar, sour cream, lemon zest, lemon juice, and lemon extract. Start on low speed, gradually increasing to medium-high. Beat until creamy, scraping down the bowl with a rubber spatula as needed to ensure all ingredients are well combined. Slowly drizzle in oil.

In a separate bowl, whisk together flour, baking powder, and salt.

Add the flour mixture to the wet mixture and mix until just combined. (Some lumps are okay.) Set aside while you prepare the cream cheese mixture.

In a medium bowl, beat cream cheese until smooth. Add in confectioners' sugar and beat until well combined.

Pour half of the batter into the prepared loaf pan, topping with half of the cream cheese mixture.

Using a butter knife, gently swirl in the cream cheese mixture.

Pour in the remaining batter and then top with the other half of the cream cheese mixture. Gently swirl in the cream cheese with the butter knife.

Bake for 75-80 minutes, or until a toothpick comes out with only a few crumbs. However, check the loaf at 45 minutes, and if it is starting to brown too much, cover it with a loose foil tent. Allow the cake to cool completely before serving (about 30 minutes).