Position oven racks in the upper and lower thirds of the oven and preheat to 350 degrees F.
Beat the butter and sugar in the bowl of a stand mixer fitted with a paddle attachment on medium-high speed until light and fluffy, about 5 minutes. Add the almond and vanilla extracts and egg and mix until combined. Reduce the mixer speed to low, add the flour and salt and mix until just combined.
Remove a quarter of the dough (about 1/2 cup) to a flour-dusted surface and reserve. Add the sprinkles to the dough left in the mixer and mix on low until just combined. Remove the dough to a flour-dusted surface and gently fold until it comes together.
Add the reserved dough back to the mixer bowl and add enough green gel food coloring to color it a vibrant green like a wreath, about 6 drops. Mix on low until the dough is completely green. Remove to a flour-dusted surface and fold with your hands until it comes together.
Tear off 2 Ping-Pong ball-size pieces of the white dough and add to the barrel of a cookie press; add 1 marble-size piece of the green dough. Repeat this pattern until the barrel is filled (you will not use all of the dough). Place a wreath disc onto the cookie press barrel according to the manufacturer's instructions. Press the cookies onto an ungreased baking sheet and set aside. Repeat 2 more times in the same pattern with the remaining dough.
Bake 2 of the batches until the cookies are firm but not yet browning on the bottom, 8 to 10 minutes. Cool the cookies for 1 minute on the baking sheets, then remove to a wire rack to cool completely, about 30 minutes. Bake the third batch and let cool. Store in an airtight container for up to a week.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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