Preheat oven to 350ºF. Grease a 9-inch Bundt pan with oil and dust lightly with flour. Shake out the excess flour.
In a stand mixer fitted with the paddle attachment (or using a hand-held mixer), beat oil and sugar on medium-high speed for 3 minutes. With the mixer running on medium-high speed, add eggs, one at a time, and mix for 5 minutes. Add the orange juice (or orange-lemon juice) and mix for another minute.
In a large bowl, sift together flour, baking powder, 1/2 tsp baking soda, and salt. Add the flour mixture to the batter and mix for 1–2 minutes, until combined. Using a spatula, fold in poppy seeds and lemon zest.
Reserve 1 cup of batter in a medium bowl and set aside. Pour the remaining batter evenly into the prepared pan.
To the reserved 1 cup of batter, stir in chocolate syrup and the remaining 1/2 tsp baking soda. Spoon the reserved chocolate batter into the pan. Using a knife, swirl the chocolate batter into the mixture.
Bake for 50–60 minutes, until the cake springs back when tapped or a skewer inserted into the cake comes out clean. Set aside to cool completely before removing from the pan.
Run a knife along the sides and center of the Bundt pan to loosen the cake from the pan. Invert the cake onto a cake plate or platter and set aside to cool.
Drizzle chocolate syrup on top and serve.
Tips
Good to Know: Use room-temperature eggs when baking for the best results. Room-temperature eggs mix into the batter more evenly, and they also create more voluminous baked goods, which is especially important in a sponge-cake like this one.
Get Organized: Instead of greasing your Bundt pan with oil, you can spray it with cooking spray. Just don’t overdo it. After spraying, I like to gently pat the inside of the pan with a paper towel to wipe away any excess oil. I like to use a fine-mesh strainer to dust the inside of the pan with 1/2 teaspoon of flour. Flip the pan over and shake out any excess flour.
Storage: Lemon–Poppy Seed Swirl Cake can be stored in the freezer for up to 1 month wrapped tightly in plastic wrap.