Heat the olive oil in a large pot over medium heat. Add the onion and carrots and cook for 5 minutes until they start to soften.
Stir in the garlic and ginger and cook for 1 minute until fragrant. Add the turmeric and stir for 30 seconds to toast the spice.
Pour in the vegetable broth, then add the lentils and pearl barley. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 35 minutes, stirring occasionally, until the lentils and barley are tender.
Stir in the spinach and cook for 2 minutes until wilted. Season with salt and black pepper to taste before serving.