Add 180 grams strawberries and 25 grams granulated sugar to a small or medium saucepan set over medium heat. Cover the saucepan, and cook until the mixture comes to a boil, about 5 minutes. Turn off the heat and let the mixture cool for 5 more minutes.
Use an immersion blender to blend the strawberries completely. Pour the strawberry mixture through a fine-mesh strainer to remove the seeds. (Note that this step is optional - You can simply mash the strawberries with a fork instead of blending, and leave the seeds with the strawberries if you choose).
Transfer the strawberry mixture to the fridge and chill for at least 30-60 minutes.
While you're waiting for the strawberries to cool, whisk together 28 grams cornstarch and 28 grams powdered sugar in a small bowl. Prepare a 9x13" baking pan by greasing it very lightly with a neutral-flavored cooking oil, then add 1-2 Tablespoons of the cornstarch mixture to the pan. Tilt the pan around to make sure the bottom and sides are covered. Tap out any excess powder and set the pan aside.
Pour the chilled strawberry mixture into the bowl of your stand mixer and stir in 113 ½ grams cold water and 1 ½ grams table salt. Sprinkle 21 grams plain gelatin over the strawberry mixture and let it bloom while you complete the next step.
Pour 300 grams granulated sugar into the center of a medium saucepan. Add 113 ½ grams cold water and 312 grams light corn syrup. Attach a candy thermometer to the side of the pot (or get your instant-read thermometer ready) and turn the heat on to medium-high. Cook until the mixture reaches 240°F, about 10-15 minutes (you can increase the heat to high if it's taking a long time, or the temperature increasing seems to stall).
Attach a whisk attachment to your stand mixer, and turn the mixer on low speed. Very carefully and slowly pour the hot sugar mixture into the mixer bowl while the mixer is running at low speed (pour it close to the side of the bowl, avoiding the whisk). When you've poured all of the hot sugar in, slowly increase the mixer speed to medium-high.
Let the mixer run until the marshmallow mixture increases in volume and becomes pale pink, glossy, and fluffy-looking, about 10-12 minutes. Add 1 gram vanilla extract and beat for 1 more minute.
Use a spatula to spread the marshmallow mixture evenly into the prepared baking pan. Rap the pan firmly on the countertop a few times to get out any large bubbles. Sprinkle some of the powdered sugar mixture evenly over the top of the marshmallows and set the pan aside to set, at least 4 hours. (Don't cover with plastic or a lid - it's best to keep it open to the air. You can cover lightly with a clean dish towel to prevent any dust from settling on it.)
Carefully remove the slab of marshmallow from the pan and transfer to a cutting board. Dust any sticky edges with the powdered sugar mixture. Use a large knife to cut the marshmallows into squares of your desired size (lightly greasing the knife with neutral-flavored oil helps to prevent sticking). Toss the cut marshmallows in the powdered sugar mixture.
If desired, dip or drizzle the marshmallows in melted milk or dark chocolate. Store the marshmallows in an airtight container or zipper bag at room temperature.