Combine the eggs, granulated sugar, honey, salt, and vanilla extract in a medium saucepan, and whisk together. Add the butter, and place the pan over medium heat. Watch the pan and whisk frequently while the mixture heats up and the butter melts. Continue to whisk until it starts to simmer, but don’t bring it to a full boil.
Once the honey mixture is hot, remove the pan from the heat and whisk in the baking powder. It will foam up and get thick and frothy. Set aside to cool until it is warm but not hot.
While you’re waiting for the honey mixture to cool, sift the flour to remove any lumps, then pour half of it out onto a cutting board or your countertop.
Stir the other half of the flour into the honey mixture, and whisk until it’s all incorporated. The batter should still be pretty runny. Scrape the batter out onto the flour on your work surface, and gently use your hands to work the flour into the dough, gently kneading it just until the flour is incorporated and the dough is mostly smooth and only a bit sticky. Flatten the dough into a disc, wrap it in plastic wrap, and refrigerate it for an hour, until firm.
Preheat the oven to 350 F. Roll the dough out onto parchment or a sil-pat, dusting with a bit of flour only if necessary to prevent sticking. Cut out 6” hearts, then use a smaller 2.5” heart cutter to cut out the middle. (Alternately, you can cut any shape you’d like out of cardstock, and trace the shape with a sharp knife onto the dough.) Re-roll the dough until you’ve cut out 12 heart shapes, to make a total of 6 cream tarts. Use excess dough to make small hearts for decorations, if desired.
Place the large hearts a few inches apart on baking sheets covered with a sil-pat or parchment paper. Bake for 6-8 minutes (I find that cookies on parchment cook faster than cookies on a sil-pat.) The cookies won’t take on any color on top, but should puff and expand a bit, and if you use a spatula to take a peek under the cookie, the bottom should be golden brown.
Let them cool completely before decorating.