If the mushrooms you are using are dried, the 20 minutes of passive time is needed to plump them up. Here's how: first, rinse the mushrooms well under cold water to clean; second, place mushrooms in a 2 cup liquid measuring cup. Add one cup of hot water and set aside for 20 minutes. Then carefully remove the mushrooms from the measuring cup.
If the mushrooms are large, slice into bite-size pieces.
Preheat the oven to 375 degrees (190 degrees Celsius).
Mix together in a large bowl the filling: cream, eggs, egg yolks, half of the cheese and half the thyme. Add the mushrooms to the filling mixture and toss to coat the mushrooms evenly.
On a baking sheet, lined with parchment paper, arrange your preferred gratin dishes. Dividing the batter evenly among the gratin dishes, top each with remaining cheese and thyme (see image).
Bake until the batter has set and is golden and bubbling, about 30-35 minutes. The Clafoutis will rise like a soufflé, so be prepared to serve immediately (the below photograph was taken about 15 minutes after coming out of the oven and the rise has disappeared). Pair with a crisp green salad tossed with homemade vinaigrette and sprinkled with left-over shavings of Parmigiano-Reggiano..