In a large pot on medium heat, add the oil and chopped onion. Sauté until the onion is translucent.
Add in the garlic, smoked paprika, thyme, marjoram, and black pepper and sauté for an additional two minutes.
Add the split peas, vegetable stock, and Worcestershire sauce to the pot.
Bring to a boil on high. Reduce heat to low, cover with lid, then simmer for 60-75 minutes, or until the peas are tender and beginning to disintegrate.
Add the potatoes and carrots into the soup. Bring to a simmer again. Simmer for 10 minutes or until the potatoes are tender.