Preheat the oven to 350°F. Butter and flour an 8.5 x 4.5 inch loaf pan and set aside.
In a medium bowl, whisk together the egg yolks, egg, heavy cream, and vanilla bean paste.
In a stand mixer bowl, sift together the flour, baking powder, and salt. Add the sugar and mix on low speed for about 20 seconds, until combined. Add the softened butter and half of the egg mixture, and beat on medium-low speed for about 3 minutes, until incorporated. Increase to medium-high speed and beat for another 3 minutes, until thick and airy. Lower the speed and gently mix in the remaining egg mixture for about 2 minutes, until just combined.
Pour the batter into the prepared pan and bake for 35 to 45 minutes, until the top is golden brown, the center no longer jiggles, and a skewer inserted into the center comes out clean.
About 5 minutes before the cake is done, mix the honey and hot water together until smooth. As soon as the cake comes out of the oven, brush the honey syrup over the top.
Let the cake cool in the pan for 20 minutes. Run a spatula around the edges, remove the cake from the pan, and let it cool on a wire rack for another 20 minutes before slicing and serving.
Store leftovers in an airtight container in the fridge for up to 4 days.
