In a large pot, boil the potatoes until they are fork-tender.
While the potatoes are coming up to a boil, preheat a deep skillet or wide, heavy-bottomed pot over medium-high heat. Add the EVOO and ground beef and crumble up the meat as it cooks, using the back of a wooden spoon or potato masher, for about 8 minutes, until brown and caramelized.
Add the onions, garlic, chili powder, cumin, smoked paprika, cinnamon, salt and tomato paste to the meat and cook another 5 minutes. Add the beer and stock, and stir to loosen any bits from the bottom of the pan. Reduce the heat and simmer for 10-15 minutes, until thickened. Season the chili with salt to your taste.
Once the potatoes are done cooking, drain and return them back to the same pot. Place the potatoes back over the heat, shaking them around a bit to dry them out. Add the butter and the whites of the scallions to the potatoes, and saut the scallions 1-2 minutes, until tender.
Remove the potatoes from the heat then add in the milk, egg yolks, salt and ground black pepper. Mash them up with the potatoes masher. Fold the cheese into the potatoes and allow it to melt.
At this point the chili should be ready to be poured into a casserole dish and topped with the cheesy scallion potatoes. Place the chili tater-topped casserole into the oven and brown the top, about 2-3 minutes. Garnish with the reserved green scallion tops and serve.