Begin by adding half of the Oreos to a food processor, layer on half of the softened cream cheese cubes, then add the rest of the Oreos and cream cheese. Pulse together on high until combined and smooth, scraping down the sides of the processor as necessary.
Line a baking sheet with wax paper. Using a 1-inch cookie scoop, scoop uniform half-spheres of Oreo mixture. Place each scoop on the lined baking sheet, flat side down, then place in the freezer for 15 minutes to firm up.
With about 5 minutes remaining of chill time, melt the chocolate in separate microwavable bowls according to the package instructions. When melted, place the bowls on your counter along with the chilled Oreo balls.
Doing so one at a time, smooth the outside of each Oreo ball and turn the flat side up towards the ceiling. It should resemble a teacup.
One by one, dip the tips of the pretzel handle in white almond bark and attach them to the sides of the cup to resemble a mug. Repeat until each Oreo ball has a pretzel handle, placing them back on the baking sheet.
Place the baking sheet back in the freezer for 15 minutes to allow the handle to harden.
When they are done chilling, ensure the chocolates are still warm and spreadable. If necessary, heat them for 30 seconds.
Dip each of the hot cocoa Oreo mugs into white chocolate, covering them completely. Then, set them on the baking tray and add sprinkles before the chocolate hardens.
Once the white chocolate has set, add a small dollop of chocolate to the top of each mug and top with marshmallow bits.
Place them back in the refrigerator for at least 1 hour to allow the Oreo balls to completely set up.