Combine mushrooms, ginger, chile, garlic, kombu, turmeric, and 4½ cups water in a medium saucepan. Bring to a simmer over medium-high heat, cover, then reduce heat to very low and cook 25 minutes to infuse broth. Strain dashi through a fine-mesh sieve into a large bowl; discard solids. Wipe out pot, pour dashi back in, and bring to a simmer.