Clean the mushrooms by wiping with a dry paper towel — do not wash them. Separate the stems, trim any bad parts, and coarsely chop the stems. Slice the caps 1/4-inch thick (halve if large) and set aside.
Make the stock: heat the olive oil and 1 tablespoon of the butter in a large pot. Add the chopped mushroom stems, onion, carrot, thyme sprig, 1 teaspoon salt, and 1/2 teaspoon pepper; cook over medium-low 10 to 15 minutes until soft. Add 6 cups water, bring to a boil, reduce heat, and simmer uncovered 30 minutes. Strain, reserving the liquid (about 4 1/2 cups; add water if short).
Meanwhile, in another large pot, heat the remaining 1/4 pound butter and add the leeks. Cook over low heat 15 to 20 minutes until they begin to brown. Add the sliced mushroom caps and cook 10 minutes until browned and tender.
Add the flour and cook 1 minute. Add the white wine and stir 1 minute, scraping the bottom of the pot. Add the mushroom stock, minced thyme, 1 1/2 teaspoons salt, and 1 teaspoon pepper; bring to a boil, then reduce and simmer 15 minutes.
Add the half-and-half, cream, and parsley; season to taste and heat through but do not boil. Serve hot.