Special equipment: a 3 1/2-inch circle cutter and a small gingerbread woman or other flat-sided cookie cutter; a piping bag fitted with a small tip or a resealable plastic bag
Preheat the oven to 325 degrees F and line 3 baking sheets with parchment paper. Dust a work surface with flour, then flatten the cookie dough into a rectangle and roll to about 1/8 to 1/4 inch thick. (If the large piece dough is hard to work with, cut it into 2 equal pieces.) Use a 3 1/2-inch circle cutter to cut as many rounds as possible (you should get about 10). Transfer to a baking sheet.
Use a 2 1/2-inch round cutter to cut the centers from the larger circles to make "O's". Using the bottom of a small gingerbread woman cutter (or other cutter with a flat base), cut the rolled center scraps into bases for the snow globes. Place the bases on the baking sheet touching the bottom of each "O" (they will fuse together when they bake). Place the cut cookies in the freezer for 20 minutes. Pat the dough scraps into a disc and chill until you can roll again and cut out more cookies to make about 1 dozen snow globes. When ready to bake, transfer the frozen cookies to 2 room-temperature baking sheets lined with parchment paper, evenly spacing 5 cookies per sheet. Bake the cookies, rotating halfway through cooking time, until crisp and golden, about 15 minutes. Transfer to wire racks to cool completely.
For the glass centers: Set up a workspace with your decorations and cooled cookies. (You will have to work fast once the glass syrup is made.) Transfer the cookies to clean pieces of parchment set on baking sheets. Stir together the sugar and corn syrup in a 2-cup or larger glass liquid measuring cup until it looks like wet sand. Microwave until the sugar is completely dissolved and is bubbling but still clear with no caramel color, about 2 to 2 1/2 minutes. Stir and microwave 30 seconds more. (This will depend on the power of your microwave, you want the syrup to be bubbling rapidly, but before it begins to caramelize).
Pour the syrup into the center of 2 or 3 cookies, letting it spread to fill the entire opening. Working quickly, while the syrup is still hot and has not yet begun to harden, sprinkle with the decorations of your choice. Continue, filling a few cookies at a time and reheating the syrup in the microwave for 5 to 10 seconds to keep it pourable, as necessary, until all of the glass centers have been poured.
For the icing: Combine the confectioners' sugar and meringue powder in an electric mixer fitted with the whisk attachment and whisk to combine. With the mixer on low, add the lemon juice and 3 tablespoons water. Mix until smooth, scraping down the sides of the bowl as needed, and add about 1 to 3 tablespoons more water, a little at a time, to make an icing that drizzles slowly from a spoon dipped into the bowl. Increase speed to high and beat until the icing is very smooth, about 1 minute. Spoon half the icing into a pastry bag fitted with a small plain tip. (Alternatively, transfer to a resealable plastic bag and snip off a corner.) Color the remaining icing in the bowl with red food coloring and transfer to another piping bag fitted with a small plain tip.
Pipe the white icing on the top of the snow globes, leaving a little in the bag to decorate the glass, if desired. Pipe the red on the bases. If desired, use the remaining white icing to pipe small snowmen in the glass part of the snow globes. Let sit until the icing hardens, 20 to 30 minutes.
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