Prepare the oven and pan. Preheat the oven to 350°F (175°C). Line an 8 × 4-inch, 1-pound loaf pan with parchment paper, allowing enough paper to extend beyond the two long sides. These overhanging edges will make it easier to remove the baked loaf from the pan.

Blend the dry ingredients. In a medium mixing bowl, thoroughly whisk together the all-purpose flour, baking powder, and salt. Set this mixture aside.

Prepare the wet mixture. Place the room-temperature eggs, whole-milk Greek yogurt, and granulated sugar in a large bowl. Using a hand mixer, beat until the ingredients form a smooth, evenly blended mixture.

Add the oil and vanilla. Pour the vegetable oil and vanilla extract into the egg and yogurt mixture. Continue beating until the oil is completely incorporated and the mixture has a uniform consistency.

Finish the batter. Gradually incorporate the prepared dry ingredients into the wet mixture while mixing on low speed. Beat only until no visible streaks of flour remain, approximately 30–60 seconds. Avoid excessive mixing, which may produce a denser loaf.

Layer the batter and cranberry sauce. Transfer half of the batter to the prepared loaf pan. Spoon approximately half of the cranberry sauce over the batter in 2–3 separate dollops.

Create the cranberry swirl. Spread the remaining batter over the first cranberry layer, then distribute the rest of the cranberry sauce across the surface in several dollops. Draw a toothpick gently through the batter a few times to produce a marbled cranberry pattern without over-swirling.

Bake the loaf. Place the pan in the preheated oven and bake for 60–70 minutes. The cake is ready when its edges are browned and a toothpick inserted into the center comes out clean. If the surface becomes too dark before the center has finished baking, loosely cover the loaf with aluminum foil during the final 20 minutes.

Cool in the pan. Set the loaf pan on a wire cooling rack and leave the cake undisturbed in the pan for approximately 1 hour.

Cool completely. Use the extended parchment paper to carefully lift the loaf from the pan. Transfer it directly to the wire rack and allow it to cool for an additional 1–2 hours before slicing.