Place Oreos in a food processor. Pulse several times, until finely crumbled.
Add vegan cream cheese to the food processor with the cookie crumbs. Pulse in short bursts to combine.
Line a baking sheet with waxed paper or parchment paper. Use a cookie dough scoop or measuring spoon to measure out small, bite-size balls. Drop these on the prepared baking sheet. Refrigerate the pan for about 30 minutes to firm up the dough.
Remove the pan from the fridge and roll the dough balls between your hands to make the balls smooth and more rounded. Return the tray to the fridge (or even the freezer) while you prepare the chocolate.
Dark Chocolate: Add dark chocolate chips to a microwave-safe bowl. Add 1 tsp coconut oil and stir together to coat chocolate chips. Heat in the microwave for 1 minute. Place a plate over the bowl in the microwave and let the chocolate set for up to 1 minute. Use oven mitts to remove the bowl and stir. If there are any unmelted chocolate bits. heat for another 20 seconds. Stir to combine.
Once the chocolate is melted, use a fork to dip one oreo ball at a time into the chocolate. Gently tap the fork on the side of the bowl to release any extra chocolate. Place the dipped truffle back on the wax paper-lined cookie tray to dry.
White Chocolate: Place the white chocolate in a microwave-safe bowl. Add 1 tsp coconut oil and stir together to coat the chips. Heat in the microwave in 20-second increments until it's melted. Stir t combine.
Once the chocolate is melted, set it aside to cool for up to a minute. Vegan white chocolate can be runny immediately after it's melted. Use a fork to dip one oreo ball at a time in the chocolate. Tap gently to remove excess chocolate and place it back on the wax paper-lined cookie tray. Note: You may need to dip white chocolate twice. To do that, let the chocolate firm up, then dip it again in melted white chocolate that is not hot.
If you want to add any decorations (like sprinkles) or crushed Oreos, do it before the chocolate firms up.
Once all the oreo balls are coated, place the tray back in the fridge to allow the chocolate to harden.
Once the chocolate is set, store oreo balls in a sealed container in the fridge for up to 10 days. They can be frozen in freezer bags for up to 2 months.
Swirly Topping for Dark Chocolate Balls: Once the chocolate coating has set on the truffles, make a simple frosting by combining 1 teaspoon coconut oil with 4 tablespoons powdered sugar. Stir this together. Then add 1 teaspoon soy milk. Stir to combine. If it's still too thick, add another 1/4 teaspoon soy milk at a time, stirring between each addition. It should be thick. Add this to a pastry bag with a #1 round Wilton tip. Add swirly lines (like an M with an extra line) to the top of each dark chocolate truffle. Let this frosting set before storing the truffles.
Swirly Topping for White Chocolate Balls: Once the chocolate coating has set, add some melted dark chocolate to a pastry bag with a #1 round Wilton tip. Add swirly lines (like a M with an extra line) to the top of each white chocolate truffle. Let this chocolate set before storing the truffles.