First, start by preheating the oven to 350F then butter and flour a 8.5x4.5 inch baking pan and set aside.
In a medium bowl, whisk the egg yolks, egg, heavy cream, and vanilla.
In a stand mixer bowl, sift the flour, baking powder, salt. Add in the sugar and mix until incorporated (about 20seconds). Add in the softened butter and half of the egg mixture and beat on medium low until incorporated (about 3 minutes.) Now increase the speed to medium high and beat for another 3 minutes in order to get a thick and airy cake batter. Lower the speed again and add the remainder of the egg mixture and gently mix until incorporated (about 2 minutes)
Pour the batter into the prepared baking sheet and bake for 35-45 minutes. You will know that the cake is ready when it no longer jiggles in the center, has a golden brown top, and a knife of a wooden skewer comes out clean when inserted in the center.
5 minutes before pulling out your tea cake loaf, prepare the honey syrup. Mix the honey the the water in a small measuring cup or bowl, and mix until you get a smooth syrup. Brush the top of the loaf with the honey syrup immediately after pulling it out. You can also drizzle it on top if you don't have a brush.
Pull the loaf out of the oven and let it cool down for 20 minutes because running a spatula around the edges, pulling it out and letting it cool down on a wire rack for another 20 minutes. Serve immediately or store in an airtight container in the fridge for up to 4 days.