Thread the marshmallows onto 2 disposable chopsticks and cook over the open flame of a stove until toasted all over, about 2 minutes. (Alternatively, line the baking sheet of a toaster oven with foil coated in nonstick spray, add the marshmallows and broil, flipping once, until golden brown, about 2 minutes per side.)
Combine the sugar and 1 cup water in a medium saucepan. Bring to a boil and simmer over medium heat until the sugar is dissolved, about 3 minutes.
Reduce the heat to low and add the toasted marshmallows to the saucepan. Cook, stirring continuously and turning down the heat if the mixture starts to bubble up around the edges of the saucepan, until the marshmallows are completely dissolved into an opaque mixture, 5 to 7 minutes.
Strain the mixture through a fine-mesh strainer and whisk in the vanilla extract and salt. Cool completely Store in the refrigerator in an airtight container for up to 1 month.
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