In a large pot or Dutch oven over medium heat, add the butter and onion. Caramelize the onions until they are a deep brown color. This should take 8-10 minutes.
Add half of the oil to the pot along with the garlic, spices, and salt. Stir for about 2 minutes, until the mixture comes together and is very fragrant.
Add in the chicken, chicken broth, and tomato paste. Cover and cook on low for about 30 minutes.
After 30 minutes, uncover, add in the soft-boiled eggs and lemon juice, and stir making sure the eggs are submersed in the sauce.
Cover and continue cooking for an additional 8-10 minutes or until the chicken has an internal temperature of 165 ℉. Serve with sides and enjoy!