In a medium bowl, add dried mushrooms and boiling water. Let sit until soft and pliable, about 5 to 10 minutes.
Transfer mushrooms to a cutting board and mince. Using a fine-mesh strainer lined with paper towel, or a coffee filter, strain liquid into a medium bowl. Set minced mushrooms and mushroom liquid aside.
In a Dutch oven or large pot over medium heat, add olive oil and heat until shimmering. Add onion, carrot, celery, minced mushrooms, and salt and pepper to taste (I like 1/4 teaspoon salt and 1/8 teaspoon pepper). Cook, stirring frequently, until the vegetables have softened, about 15 to 20 minutes.
Stir in garlic until fragrant, about 30 seconds. Stir in strained mushroom liquid and water, scraping up any browned bits from the bottom of the pot.
Add tomatoes and their juice, kale, and chickpeas and stir to combine (add kale in batches if it doesn't immediately all fit in the pot). Bring to boil; reduce heat, cover, and simmer until kale is almost tender, about 10 to 15 minutes.
Stir in orzo and simmer until the pasta is tender, about 5 to 7 minutes. Season to taste with salt and pepper (I like 2 teaspoons salt and 1 teaspoon pepper). Garnish with red chili flakes if desired.