Line large baking sheet with parchment paper and set aside. If necessary, clear space in freezer to allow baking sheet to sit level.
Add 2 cups vegan semi-sweet chocolate chips and 2 tablespoons vegan shortening to medium microwave-safe bowl, then place bowl in microwave. Microwave ingredients 60 seconds at 50% power.
Remove bowl from microwave and stir chocolate and shortening together, then return bowl to microwave. Microwave ingredients 30 seconds on 50% power. Repeat process, stirring mixture well after each 30-second burst, until chocolate and shortening are fully melted and combined into smooth mixture. Be very careful not to over-microwave.
Once chocolate mixture is smooth, remove bowl from microwave. Add 1 ½ teaspoons peppermint extract to mixture and stir to incorporate.
Place one Ritz cracker in bowl of melted chocolate. Using fork, flip cracker over in chocolate until all sides are thoroughly coated.
Carefully lift chocolate-covered cracker out of melted chocolate and hold over bowl to allow excess chocolate to drip off. Transfer chocolate-covered cracker to prepared baking sheet. Note: for smoother cookie edges, scrape bottom of cracker against edge of bowl first to remove excess chocolate, then place cookie on baking sheet..
Repeat process until all 36 Ritz original crackers have been dipped in chocolate and placed on baking sheet in one even layer, making sure cookies do not touch or overlap.
Place filled baking sheet in freezer. Freeze cookies 10 minutes or until chocolate shell has hardened.
Once chocolate has hardened, transfer cookies to sealable freezer bag or airtight freezer-safe container. Serve cookies chilled and store extra cookies in refrigerator or freezer to keep chocolate hard.