Prep your vegetables. Dice the onion and potato, slice the carrots and celery, mince the garlic, and chop the greens.
Rinse the barley under cold water to remove excess starch.
Sauté the aromatics (optional but worth it). In a skillet, warm the olive oil over medium heat. Cook the onion, carrot, and celery with a pinch of salt for 5–7 minutes until softened. Stir in the garlic for 30 seconds. This step deepens flavor, but you can skip and add everything straight to the slow cooker if you’re short on time.
Load the slow cooker. Add the sautéed veggies (or raw), barley, potato, crushed tomatoes, vegetable broth, bay leaf, thyme, oregano, and smoked paprika.
Stir to combine.
Cook low and slow. Cover and cook on Low for 6–7 hours or High for 3–4 hours, until the barley is tender and the potatoes are soft. If the soup thickens too much, stir in 1–2 cups warm broth or water.
Finish with greens and peas. In the last 15 minutes, stir in the kale or spinach and the frozen peas. Cook until the greens wilt and the peas are warmed through.
Brighten and season. Remove the bay leaf.
Stir in lemon juice. Taste and adjust with salt and pepper. The lemon lifts the flavors and balances the starchiness.
Garnish and serve. Ladle into bowls and top with chopped parsley and a drizzle of olive oil if you like.
Serve with crusty bread for dipping.