Prepare a 9x13" baking pan by lining it with parchment paper. Cut a piece of parchment paper about 4 inches larger than the bottom of the pan. Trace around the bottom of the pan with a pencil, and make creases where the lines are. Cut slits in each of the 4 corners, so that the paper folds around the edges nicely.
Melt 2 Tablespoons unsalted butter in a small saucepan over medium heat. Add 14 ounces sweetened condensed milk and stir to combine. Continue heating, stirring very often, until the sweetened condensed milk is heated through, but not boiling. Reduce the heat to low.
Stir in the chopped unsweetened chocolate and the chopped dark or semi-sweet chocolate. Continue stirring constantly until the chocolate is completely melted and no lumps remain. Remove the saucepan from heat and stir un 2 Tablespoons Maraschino cherry syrup until it's completely incorporated. Allow the chocolate mixture to cool slightly.
Meanwhile, toss 14 ounces mini marshmallows and 1 cup quartered maraschino cherries together in a large bowl. Once the chocolate is slightly cooled, (it's ok if it's still warm, but shouldn't be hot) pour the chocolate over the marshmallow mixture. Stir with a spatula until all of the marshmallows are evenly coated with chocolate.
Pour the chocolate marshmallow mixture into the prepared baking pan. Press the mixture into all the corners, and smooth the tops as much as possible. Cover the pan with plastic wrap and place it in the fridge to set, about 1-2 hours. Remove the squares from the pan and peel away the parchment paper. Cut into squares using a large, sharp knife. Serve immediately, and/or store any leftovers in an airtight container or zipper bag in the fridge or freezer.
Notes
Sweetened condensed milk appears to be sold by weight in the US (14 ounces or 397 grams), while it's mostly sold by volume in Canada (300mL or 10 fluid ounces). Since sweetened condensed milk is heavier than water, both cans are the same size.You will need a jar of maraschino cherries that is at least 250mL (8oz). My jar was this size, and the cherries just filled a cup. If you want to be sure you have enough, or plan to use the leftovers for something else, choose a larger jar or get two.