Heat a large skillet over medium-high heat. Add a splash of oil, then saute the onion and mushrooms until the mushrooms release their liquid and start to brown, about 6 minutes. Add the garlic and tomato paste; cook 1 minute more until fragrant and the paste darkens slightly.

Pour in the red wine (if using) and scrape up any browned bits from the pan. Let bubble for 30 seconds, then remove from heat.

Place the potatoes, carrots, and celery in the slow cooker. Add the onion-mushroom mixture, thyme, smoked paprika, bay leaves, and vegetable broth. Stir gently to combine.

Cover and cook on LOW for 8 hours or HIGH for 4 hours, until the potatoes and carrots are fork-tender but not falling apart.

Stir in the frozen peas and let sit for 5 minutes to warm through. Remove the bay leaves. Taste and add salt and pepper as needed - start with 1 teaspoon salt and go from there depending on your broth.

Ladle into bowls and sprinkle with fresh parsley. Serve with crusty bread if desired.