Place the butter and sugar in a large bowl, then use a hand or stand mixer set on medium to blend them until they're light and fluffy. Add the egg and honey and blend well.
In another bowl, whisk together the flour, baking powder, and salt. With the mixer set on low, add the flour mixture to the other ingredients, a third at a time, blending well. If the dough is too soft, add more flour, up to three tablespoons.
Heat the oven to 350° and line two baking sheets with parchment paper. Place the dough between two parchment sheets and roll it into an 1/8-inch-thick circle.
Form the dough into shapes using mini animal-cookie cutters . Place the cookies on the baking sheets, spacing them a half inch apart. Bake until the edges of the cookies begin to brown, about 10 minutes. Let them cool on the baking sheets for 10 minutes, then transfer them
to a rack to cool completely.