Finely chop (and peel if necessary) the onion, carrots, and potato. Mince the garlic.
In a large pot, add the oil and butter and heat over medium high heat. Stir in the onion and carrots. Season with salt and pepper. Cook for 2 minutes until they begin to soften. Then add the potato and garlic. Sprinkle on the cumin and cayenne. Cook another minute. Then add the split peas, bay leaves, and stock.
Reduce the heat to low and cover the pot. Cook for 1 hour. Check to see if the peas are fully cooked, they should be very soft and beginning to lose their shape somewhat. If they still seem firm, cook for another 10-20 minutes or more.
Remove from the heat once fully cooked and remove the bay leaves. Taste and add more salt and pepper if needed. Garnish with cheese, fresh herbs (I had some thyme on hand) and crackers for serving. These are all optional!
If you want to make this vegan, simply use vegan butter or two tablespoons of olive oil instead of a mix of olive oil and butter. And skip the cheese at the end or use a vegan cheese.
This soup makes great leftovers but it will become very thick when cold. When you reheat, if the soup doesn't thin out as much as you would like, add a tablespoon or two (per serving) to the final soup.