Preheat your oven to 325°F (163°C).
Grease your loaf pan with butter and lightly dust it with flour, or use parchment paper.
In a large mixing bowl, beat the unsalted butter and superfine sugar together until light and fluffy (about 5 minutes).
Add the cream cheese to the butter and sugar mixture, and mix until smooth.
Add the eggs and egg yolks one at a time, mixing well after each addition.
Pour in the half-and-half and vanilla extract, mixing until well combined.
In a separate bowl, whisk together the all-purpose flour and salt. Gradually add this to the wet ingredients, mixing just until combined.
Transfer the batter into the prepared loaf pan, smoothing the top with a spatula.
Bake for about 70-80 minutes, or until a toothpick inserted comes out clean.
Let the cake cool in the pan for about 15 minutes before transferring it to a wire cooling rack.