Add butter, powdered sugar, salt, vanilla extract, and almond extract to the bowl of a large food processor. Process until smooth (about eight 1-second pulses). Add flour and pulse until mixture looks crumbly and chunky (about six 1-second pulses). Add sprinkles and quickly pulse several more times, until the sprinkles are just evenly incorporated.
Turn the dough out onto a work surface and shape into a rough ball. Cut ball in half and form each piece of dough into a 7 ½- to 8-inch long log. Tightly wrap each log in plastic wrap and freeze for 30 minutes (or refrigerate for at least 4 hours and up to a week).
Place rack in center position of oven. Preheat oven to 350°F. Line two baking sheets with parchment paper. Remove one log of dough from the freezer (or refrigerator). Cut dough into ¼-inch to ⅓-inch thick slices, rolling log every few slices to maintain the round shape of the cookies. Arrange cookies on lined baking sheet. Bake until cookies just barely turn a light golden color around the edges, between 10 and 15 minutes. Allow to cool on baking sheets.
Repeat steps with the second log of cookie dough. Once cookies are completely cool, store in an airtight container.
BE SURE TO MEASURE YOUR INGREDIENTS CAREFULLY. The powdered sugar and flour should be fluffed and spooned into the measuring cup, then leveled off. If the dry ingredients are packed down when you measure them, or if your measuring cup is overflowing, the cookie dough will turn out crumbly.
If you wish, this recipe will work using an electric mixer instead of a food processor.
To achieve round logs of dough, I shape them the best I can and then lightly roll them on the counter like a rolling pin after they're wrapped in plastic wrap.
While the first sheet of cookies is baking, take the second log of cookie dough out of the freezer, slice it, and arrange cookies on second cookie sheet so that it's ready to pop in the oven as soon as the first sheet comes out.
This recipe is great for make-ahead treats. The cookie dough can be made ahead of time and then sliced and baked when you're ready. Since this dough is formed into logs, wrapped in plastic wrap, and chilled before baking, you can refrigerate it for up to a week or freeze it for even longer (although I'd recommend sticking the wrapped logs in a freezer-thickness gallon-sized baggie for extra protection from freezer burn).
If you freeze your shortbread logs long enough to freeze solid, you'll need to let them thaw in the fridge (preferably overnight) before slicing and baking.
For a special touch, you can drizzle or dip these cookies in melted white, dark, or milk chocolate.