Preheat the oven to 325°F (160°C). Grease the bottom and sides of a 9x5-inch loaf pan, then dust the pan with flour.
Sift together the flour, baking powder, and salt into a medium bowl, then set aside.
Cream the butter in a mixer at medium speed until very creamy, about 2 minutes. Gradually add the sugar and continue beating for about 4 minutes until the mixture is very light and fluffy. Reduce the speed to low and add the eggs one at a time, beating well after each addition and scraping down the sides of the bowl occasionally.
Add the lemon zest and vanilla extract. Mix in the flour mixture at low speed in three additions, alternating with the heavy cream in two additions, mixing just until the flour is incorporated. Scrape the batter into the pan and smooth the top.
Bake for 60–70 minutes, or until a cake tester inserted into the center comes out clean. Remove from the oven and let cool on a wire rack for 20 minutes. Slice into pieces and serve.