Step #1 In a bowl, mix shiitakes & 1 c hot water; let this stand until shiitakes are soft, 7 to 10 mins.
Step #2 As shiitakes soak, peel onion, shallot, & garlic.
Step #3 Finely chop in a food processor/blender or with a knife.
Step #4 In a 10- to 12-inch frying pan over medium-high heat, olive oil, shallot, & paprika until vegetables begin to brown, garlic, frequently stir onion, 5 to 7 mins.
Step #5 Meanwhile, trim off & discard discolored stem ends of common mushrooms.
Step #6 Finely chop mushrooms in a food processor/blender or with a knife.
Step #7 When shiitakes are soft, squeeze in soaking water to release grit, lift out, & squeeze dry; reserve water.
Step #8 Trim off & discard stems; finely chop shiitakes in a food processor/blender or with a knife.
Step #9 Add common mushrooms, shiitakes, & thyme to onion mixture.
Step #10 Slowly pour reserved soaking water into pan, leaving sediment behind.
Step #11 Stir often over high heat until mushrooms begin to brown, 8 to 10 mins.
Step #12 Remove from heat & let cool, about 10 mins.
Step #13 Add yogurt, salt, & pepper to taste.
Step #14 Spoon into a bowl & sprinkle with parsley.