Cream butter, brown sugar, and white sugar in a bowl. Mix in egg yolks, lavender, vanilla, and almond extract until combined.
Whisk together flour, cornstarch, and salt in a separate bowl. Add to butter mixture and mix to combine.
Roll dough into 1-inch balls and place 2 inches apart on the prepared baking sheets. Use your thumb (or another utensil, like the bottom of a shot glass) to make indentations in the center of each cookie. Add enough lemon curd to completely fill each indentation. Place baking sheets in the refrigerator to chill for 20 minutes.
Preheat the oven to 375 degrees F (190 degrees C).
Remove baking sheets from refrigerator and lightly drizzle each cookie with honey.
Bake in the preheated oven until cookies begin to turn golden brown, 10 to 12 minutes. Allow to cool on baking sheet for several minutes before transferring to cooling rack.