For swirls, which must be piped quickly, halve the recipe and then repeat.
For cut-out rounds, coat a 13-by-9-inch glass baking dish with cooking spray. For swirls, line 2 rimmed baking sheets with parchment paper. Set aside. Sift together confectioners' sugar and cornstarch in a medium bowl; dust half of the mixture over prepared dish or sheets.
Put granulated sugar, corn syrup, and 3/4 cup water into a small saucepan. Bring to a boil over high heat, stirring to dissolve sugar. Cook, without stirring, until syrup registers 240 degrees on a candy thermometer.
Meanwhile, put 3/4 cup cold water into the bowl of an electric mixer; sprinkle with gelatin. Let soften 5 minutes.
Attach bowl with gelatin to mixer fitted with the whisk attachment. Beat on medium speed 1 minute. Reduce speed to medium-low. With mixer running, add hot syrup, pouring down side of bowl. Raise speed to medium-high; beat until fluffy, opaque, and cool, 7 to 10 minutes. Beat in extract or liqueur. Add food coloring, 1 drop at a time, until desired shade.
For cut-out rounds, transfer mixture to prepared dish; smooth with an offset spatula. For swirls, transfer mixture to a pastry bag fitted with a 1/2-inch plain round tip (such as Ateco #808); pipe 1 1/2-inch swirls onto prepared sheets, spacing about 2 inches apart. Sift remaining confectioners' sugar mixture over tops.
Let marshmallows set at least 4 hours (up to overnight). For rounds, unmold, then cut out with a lightly oiled 1 3/4- or 2-inch cutter. Dust with confectioners' sugar. Marshmallows can be stored in airtight containers up to 1 week.