Rinse both the green and yellow split peas thoroughly under cold water, picking out any debris. Set aside.
Heat 1 tablespoon olive oil in a large Dutch oven over medium heat. Add the onions and cook until translucent, about 5 minutes.
Add the carrots and celery to the pot and cook for another 5 minutes, stirring occasionally.
Add the minced garlic and cook until fragrant, about 1 minute.
Add the remaining tablespoon of olive oil and the rinsed split peas to the pot, stirring to coat with oil.
Pour in the vegetable broth and add bay leaves, thyme, oregano, and smoked paprika. Stir to combine.
Bring the mixture to a boil, then reduce heat to low. Cover and simmer for about 2 hours, stirring occasionally, until peas have broken down and soup has thickened.
Remove bay leaves and stir in the apple cider vinegar, which brightens the flavors.
Season with salt and pepper to taste.
For a smoother texture, use an immersion blender to partially blend the soup, or leave as is for a more rustic texture.
Serve hot, garnished with fresh parsley.