Line an 8x8 inch baking pan with parchment paper, leaving an overhang on all sides. Lightly grease the parchment paper.
In a small saucepan, combine granulated sugar, corn syrup, and water. Heat over medium heat, stirring until sugar dissolves. Cook without stirring until the mixture reaches 240°F (115°C) on a candy thermometer.
While the syrup is cooking, whip the egg whites with cream of tartar in a clean, dry bowl of a stand mixer until soft peaks form.
Once the syrup reaches 240°F, slowly and carefully pour it in a thin stream into the whipping egg whites while the mixer is running on medium-high speed. Continue to whip until the mixture is thick, glossy, and has cooled to room temperature (about 10-15 minutes).
Fold in the strawberry puree and vanilla extract until just combined.
Pour the marshmallow mixture into the prepared pan and spread evenly. Let it set at room temperature for at least 4 hours, or preferably overnight.
Combine powdered sugar and cornstarch in a small bowl. Dust your work surface and a sharp knife or pizza cutter with the mixture.
Lift the marshmallow slab out of the pan using the parchment paper overhang. Cut into desired shapes. Dust all sides of the marshmallows with the powdered sugar-cornstarch mixture to prevent sticking.
Notes
Store marshmallows in an airtight container at room temperature for up to 1 week.