Pour vodka into a ½-gallon glass canning jar with lid; set aside.

Place oven rack 6-inches from heat. Preheat broiler to HIGH. Arrange marshmallows on a large baking sheet. Broil 30 to 60 seconds or until golden brown, turning halfway through. Cool completely.

Add cooled toasted marshmallows and vanilla bean to jar; gently stir to combine. Place lid on jar. Store at room temperature for 3 to 7 days, turning jar occasionally.

To strain, line a fine-mesh sieve with cheesecloth; set sieve over a bowl. Strain vodka mixture through cheesecloth-lined sieve. Discard marshmallows and vanilla bean. If necessary, repeat straining until vodka is no longer cloudy. Store strained vodka in a tightly covered clean jar in refrigerator for up to 1 month. Use in your favorite cocktails.