In a large dutch oven or soup pot, heat 1 tbsp oil over medium heat. When the pot is hot, add onions, carrots and celery. Season with salt and pepper. Cook for 5-7 min, stirring occasionally, until tender.
Add garlic, tomato paste, thyme, oregano and paprika (and chili flakes or cayenne, if using). Cook for another 2-3 min, stirring often, until fragrant and toasted.
To the pot, add sweet potatoes and barley, stir to coat. Then add bay leaves, diced tomatoes and vegetable broth. Season well with salt and pepper. Bring to a simmer. Once simmering, reduce heat to medium-low. Simmer uncovered for 20 min.
Stir in spinach. Season with salt and pepper, to taste.
Divide soup between bowls. Sprinkle with parsley, if desired.