Heat vegetable oil in a large pot over medium heat. Cook and stir bacon in hot oil until browned and crisp, 5 to 7 minutes. Add onion, carrots, celery, and salt; cook and stir until onion is softened and translucent, about 10 minutes. Season with black pepper, cumin, thyme, and cayenne pepper.
Pour lentils into bacon mixture and stir until completely coated in rendered bacon fat. Add chicken broth and bay leaf; bring to a simmer. Reduce the heat to low and cook, adding more chicken broth as needed, until lentils are tender, 45 minutes to 1 hour.
Season with salt, black pepper, and cayenne pepper to taste. Stir in 3 tablespoons parsley.
Ladle soup into bowls, sprinkle remaining parsley over top, and drizzle with extra-virgin olive oil.