Combine blueberries, 1/2 cup of sugar, water, lemon juice, ginger, and salt in a saucepan over medium heat. Simmer for 10 minutes or until berries are softened and starting to burst.
Remove from heat and transfer to a blender (use caution when blending hot liquids; feel free to work in batches or let the mixture cool slightly before blending).
Blend blueberry mixture until smooth. For a smoother final product, strain it through a fine mesh sieve to remove any tiny bits of skin and seeds.
Whisk guar gum with 1 tablespoon sugar, then add to blender and puree until incorporated.
Transfer sorbet base to a heat-safe container or 4-cup glass measuring cup. Cover tightly and refrigerate until completely chilled, at least 3-4 hours or ideally overnight.
Churn in an ice cream maker according to manufacturer’s instructions. Transfer to a freezer-safe container. Cover, pressing down plastic wrap or parchment paper onto the sorbet surface to prevent freezer burn, and freeze overnight until firm.