Place the potatoes in a large pot, cover with room temperature water and season liberally with salt. Bring to a boil over high heat. Reduce to a simmer and cook until fork tender. Drain the potatoes, saving 1/2 cup of the cooking water for thinning out if needed.
Pass the potatoes through a food mill into a large bowl. Add the butter and heavy cream, and fold together with a spatula until combined. Fold in the shredded cheese. If the potatoes get too thick, thin them out with a little of the cooking water. Add salt and pepper to taste. Serve garnished with chives and a drizzle of olive oil.
For the onion confit: Heat a large enameled cast-iron pot over medium heat. Add the butter; when it begins to foam, add the red onions, marjoram, thyme, bay leaves and sugar, and sprinkle liberally with salt. When the onions begin to caramelize, add the red wine and balsamic vinegar and reduce to dry. Reduce the heat to medium-low and add 1 cup of the beef stock; cook until reduced to a glaze. Repeat until all the beef stock has been used. Turn off the heat and adjust the seasoning with salt and pepper.
For the rib-eye: Heat a 12-inch cast-iron skillet over high heat; add the oil. Pat the steak dry with paper towels, and sprinkle liberally with salt and pepper. When the oil is just below smoking, place the steak into the pan. Once a nice sear has developed, flip the steak and add the butter, thyme and garlic. If the garlic or steak begins to burn, reduce the heat. Cook, basting the steak with the bubbling butter, until an internal temperature of 125 degrees F has been reached for medium-rare. Remove the steak to a cutting board and let rest for 7 to 10 minutes before slicing. Serve with the French onion confit.