In the bowl of a mixer fitted with the paddle attachment, beat butter until fluffy, 3 to 5 minutes. Add sugar, and continue to beat until pale and fluffy, occasionally scraping down the sides of bowl, about 2 minutes more. Beat in vanilla.
Add flour, artichoke, bell pepper mixture, and mix on low speed, scraping sides if necessary, until flour is just incorporated and dough sticks together when squeezed with fingers.
Turn out dough, forming into 2 disks; wrap each in plastic. Refrigerate until firm, at least 1 hour.
Preheat oven to 225 degrees. Roll out 1 disk to a 1/4-inch thickness. Cut out shapes using desired cookie cutter, and transfer to prepared baking sheets. Reroll scraps. Repeat with remaining disk. Indent cookies with desired stamps. Refrigerate until firm, at least 30 minutes. Bake until firm and golden, 13 to 15 minutes. Let cool completely on a wire rack.