Preheat the oven to 350°F (180°C) and position a rack in the middle of the oven. Have a non-stick 9×5-inch loaf pan ready.
In a medium bowl, whisk together 2 cups all-purpose flour, 2 1/2 teaspoons baking powder, and 1/4 teaspoon salt. Set aside.
In a large mixing bowl, beat 11 tablespoons butter (room temperature) and 3/4 cup granulated sugar until pale and fluffy, about 3–5 minutes with an electric mixer on medium speed.
Add 2 tablespoons neutral-tasting oil and mix until incorporated.
Add the 3 large eggs one at a time, mixing briefly after each egg until combined.
Stir in the zest of one lemon and 2 teaspoons pure vanilla extract until evenly distributed.
Add the flour mixture to the wet ingredients in two additions, mixing on low speed or folding with a spatula just until no dry streaks remain. Do not overmix.
Add 2 tablespoons milk and mix only until the batter comes together into a soft, scoopable loaf batter.
Fold in 2 teaspoons caraway seeds until evenly distributed.
Spoon the batter into the prepared non-stick 9×5-inch loaf pan and smooth the top with a spatula or the back of a spoon.
Bake on the middle rack for 45–55 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Let the cake rest in the pan for 5 minutes, then remove it from the pan and transfer to a wire rack to cool completely.