Preheat oven to 350 degrees F (175 degrees C). Line a rimmed baking sheet with parchment paper.
Toss strawberries with 1/2 cup sugar in a large bowl until thoroughly combined. Spread on the lined baking sheet.
Bake in the preheated oven until tender, golden brown, and fragrant, about 10 minutes. Cool to room temperature, about 15 minutes.
Transfer strawberries to a blender; puree until smooth. Press puree through a fine-mesh strainer using a spoon; discard seeds and pulp.
Combine remaining 1/4 cup sugar and xanthan gum in a small bowl.
Pour water into a small saucepan. Add sugar mixture and whisk vigorously until very smooth. Stir in corn syrup. Cook over medium heat, stirring often, until sugar dissolves fully, about 3 minutes. Remove from heat and whisk in strained strawberry puree and coconut cream.
Transfer mixture to an airtight container and refrigerate until cold, at least 4 hours and up to 24 hours.
Pour chilled mixture into an ice cream maker and churn according to manufacturer's instructions until it reaches soft serve consistency, 15 to 25 minutes.
Scoop soft serve into a piping bag using a spatula; pipe into ice cream cones.