In a large pot, heat half of the olive oil over medium heat. Add the shiitake mushrooms and diced poblano chile, stirring occasionally for 5-6 minutes until golden brown; remove and set aside.

In the same pot, add remaining olive oil, place turkey breast skin-side down, brown for 5 minutes, seasoning with salt and pepper.

Pour in enough cold water to cover the turkey, add chopped onion, celery, carrot, and a grated garlic clove. Simmer, cover, and cook for about 1 hour.

Remove turkey, shred into bite-sized pieces, add baby potatoes to the broth, cooking for an additional 25-30 minutes.

Return shredded turkey, sautéed mushrooms, and fresh thyme to the pot, stir gently and adjust seasoning.

In a separate skillet, melt a tablespoon of butter, whisk in flour to create a roux, cooking for about 2 minutes. Add to soup while whisking, then pour in heavy cream and heat for 3 minutes.

Ladle soup into bowls, garnish with fresh parsley or thyme, and serve with Worcestershire sauce on the side.