Rehydrate shiitake: Add dried shiitake mushrooms and water to a bowl. Set aside for a few hours to rehydrate the shiitake. If you're short on time, you can use boiled water to speed up the process.
Strain shiitake and liquid: Remove the rehydrated shiitake from the liquid but SAVE the liquid as we will be using this in the next step. Set a strainer over a bowl and pour the liquid into the strainer to get rid of any dirt or rocks that were on the mushrooms.
Blend mushroom mixture: Add mushrooms, reserved liquid, miso, salt, garlic, ginger, and soy sauce to a blender and blend until smooth.
Make caramel: Add sugar and water to a saucepan over low heat. Stir constantly until sugar dissolves. Raise the heat to medium and stop stirring. Boil the mixture until it turns amber in color.
Add mushroom mixture: Lower heat to medium low and pour in the blended mushroom mixture, whisking until combined. Simmer for 2-3 minutes.
Thicken: Whisk together cornstarch and water. While stirring, pour the cornstarch slurry into the mushroom sauce. Continue stirring until the mixture thickens, then remove from heat.
Cool: Let the stir fry sauce cool in the pan for 5 minutes, then transfer the sauce to jars to finish cooling. Lightly cover the jars with a breathable towel to prevent the top from drying out. Once cooled, cover the jars and store in the fridge for up to 2 weeks (or freeze in ice cube trays).