In a large saucepan, heat 2 tsp. oil over medium-high heat; add onion, carrots, and celery. Cook, stirring occasionally, for 3 minutes, or until onion is translucent. Add garlic; cook, stirring frequently, for 1 minute.
Add wine and tomato paste; cook, stirring frequently, for 3 minutes.
In a small bowl, combine miso paste with a small amount of broth and whisk with a fork to make a thinner paste. Set aside.
Add vegetable broth, miso paste mixture, thyme, paprika, garlic powder, salt, pepper, and bay leaves to pan. Bring to a simmer; cook for 30 minutes.
While stew cooks, heat remaining 2 tsp. oil in a large skillet over high
heat until first wisps of smoke appear. Add mushrooms; cook for 5 minutes, stirring occasionally, to let mushrooms brown. Work in batches, if necessary, so as not to overcrowd pan. Add seared mushrooms to stew.
Add cornstarch mixture; mix well. Cook for 1 minute, or until stew has thickened slightly. Remove from heat. Discard bay leaves.
Divide evenly among five serving bowls. Garnish evenly with parsley.
Serve immediately, or store refrigerated in an airtight container for up to 5 days.