Preheat your oven to 325°F (160°C) to ensure even baking and a perfect golden crust.
Grease your 9x5 inch loaf pan generously with butter or non-stick spray, then line the bottom with parchment paper for easy removal after baking.
In a large mixing bowl, combine the unsalted butter and superfine sugar. Using an electric mixer, beat on medium speed until the mixture is light and fluffy, about 5 minutes.
Add the cream cheese to the butter-sugar mixture and beat until fully incorporated, adding richness and moisture to the cake.
Add the large eggs and egg yolks one at a time, mixing well after each addition to ensure a smooth batter without lumps.
Pour in the half-and-half and vanilla extract, mixing until well combined for added richness and flavor.
In a separate bowl, whisk together the all-purpose flour and salt. Gradually add this dry mixture to the wet ingredients, mixing on low speed until just combined. Avoid overmixing; a few flour streaks are okay.
Pour the batter into your prepared loaf pan, smoothing the top with a spatula. Bake in the preheated oven for 75-90 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool in the pan for about 15 minutes. Then, transfer it to a cooling rack to cool completely before slicing.