Combine flour, ground oats, and baking soda in small bowl. Mix to combine.
Beat butter, sugar, honey, & vanilla in mixer bowl until combined. Add flour mixture to butter mixture, mixing just until combined.
Divide dough in half. Form each half into a flat disk, wrap in plastic, and refrigerate 1 hour.
Preheat oven to 350F. Grease baking sheets or line with parchment paper.
Working with one disk of dough at a time, turn dough out onto a lightly floured surface. Roll dough out to approximately ¼" thickness. Cut as desired, and transfer cookies to baking sheets, placing about 1" apart. Scraps can be gathered and re-rolled.
Bake 6-8 minutes or until lightly browned, rotating the cookie sheets at the halfway point. Cool on baking sheets until set, then remove cookies to a cooling rack to cool completely.
Notes
Note on oats: I used my food processor to pulverize the rolled oats as finely as it could manage. The result was tasty, but you can definitely see specks of oats throughout the dough. If that isn't what you want (or you just don't feel like dirtying your food processor), you can use oat flour instead (available [here] on Amazon).Note on cook time: I love my tiny cookie cutters (available [here]), but if you're using larger cutters, the cookies will take longer to brown. That said, I also used a silpat (available [here]), which causes the cookies to brown more slowly than if you just grease a cookie sheet or use parchment. My small cookies on a silpat were browned in 6 minutes. You'll just want to keep an eye on yours so you don't end up with burnt elephant trunks and giraffe necks. ;)