In a large saucepan, heat 3 tablespoons oil over medium-high heat until shimmering. Add onion and 1 teaspoon salt and cook until onion is soft and translucent, about 7 minutes. Add carrots, garlic, oregano (if using), and remaining 1 tablespoon olive oil and cook, stirring frequently until fragrant, 2 minutes.
Add chickpeas, miso-water, and remaining 1 teaspoon salt and stir to combine. Add enough water to cover ingredients by approximately 1 inch. Reduce heat to medium-low and simmer with lid ajar until flavors meld and carrots are softened, about 30 minutes. Season with salt to taste.
Using a ladle, add approximately half of stew to blender. Cover blender, remove center vent, and cover with a clean kitchen towel. Starting at low speed and slowly progressing to high speed, blend until smooth, then stir back into stew. Simmer on medium-low heat, uncovered, until thickened to a bisque-like texture, 20 to 30 minutes; be sure to stir occasionally to prevent sticking at bottom of pot.
Serve with lemon wedges and a generous drizzle of olive oil.
