In a separate bowl or measuring cup, whisk the molasses into the hot water until fully dissolved, then whisk in the sour cream until smooth.
⅔ cup 227g unsulphured or dark molasses (not blackstrap), ½ cup 120ml hot water (about 100°F)
In a large bowl, beat the butter, oil, and brown sugar on medium-high for about 2 minutes, until creamy and lighter in color.
6 tablespoons 85g unsalted butter, softened, 2 tablespoons 28g neutral oil, ½ cup 100g packed dark brown sugar
Beat in the egg, egg yolk, and vanilla, scraping down the bowl.
1 large egg, 1 large egg yolk, 1 teaspoon pure vanilla extract
Add the sour cream and mix. It's okay if it looks a tad curdle, once you add the flour it will smooth out.
¼ cup 60g sour cream, at room temperature
On low speed, add about a third of the dry ingredients, then half the molasses mixture. Repeat, ending with the dry ingredients. Mix just until no dry streaks remain. The batter will be thin.
Pour into the prepared pan and bake for 55-60 minutes, starting to check at 50. It’s done when a toothpick comes out with a few moist crumbs, not completely clean.
Let the cake cool in the pan for about 20 minutes, then cover the pan tightly with foil while it’s still warm. Let it finish cooling covered.
For the cream cheese frosting
In a large bowl, beat the butter on medium speed for about 1 minute, until smooth and creamy.
¼ cup unsalted butter
Add the cream cheese and beat for another 30 to 60 seconds, just until fully combined and lump-free. Don’t overbeat here, or the frosting can turn runny.
4 oz Philadelphia full fat cream cheese
Add the powdered sugar and mix on low until it’s incorporated, then increase to medium and beat for about 1 minute, until light and fluffy.
1 cup powdered sugar
Add the vanilla bean paste and salt and beat just until combined.
½ teaspoon vanilla bean paste, ¼ teaspoon salt
Make sure the loaf is completely cooled before frosting.
Spread over the completely cooled cake or loaf. If the frosting feels too soft, chill it for 15 to 20 minutes before using.