Make the peas: Soak the peas overnight in water. The next day, in a separate pot, cook the country ham over medium-high heat and let the fat render out. Add the diced carrot, celery, onion and shallot, and sweat in the ham fat until tender.
Drain the peas from the soaking liquid and add them to the pot. Add enough fresh water to cover the peas by 2 inches. Bring to a simmer and add the garlic, bay leaves and salt to taste. Simmer until the peas are tender, about 1 hour. Remove from the heat and let cool in the cooking liquid, or pot likker.
Meanwhile, make the confit egg yolks: Preheat the oven to 149°. Carefully place the egg yolks in a shallow pan and cover with enough olive oil to fully submerge them. Place them in the oven for 1 hour and 15 minutes. Reserve until ready to plate.
Make the crispy collard greens: Preheat the oven to 350°. Bring a large pot of water to a boil and prepare an ice bath. Blanch the collard greens for 45 seconds, and then transfer to the ice bath to chill. Drain and dry thoroughly.
Place the greens on a sheet pan in the oven and turn the oven off. Leave the collard greens in the oven for at least 8 hours or overnight.
To assemble: Spoon the peas into a serving dish along with some of the pot likker and top with a confit egg yolk. Finish with a few leaves of the crispy collard greens. And serve.