Growing up in New York, you co-opt quintessential dishes from the city's other immigrants. I'm Italian-American, but I have legacy recipes for chopped liver and corned beef and cabbage. My mother makes corned beef and cabbage the way she saw it made while growing up in Queens. It's easy and straightforward with, as she says, "just one secret." Garlic. She makes cuts all over the corned beef and inserts slivers of fresh garlic — it pumps up the flavor.
Melt the butter in a large pot over medium to low heat. Then add enough oil to just cover the bottom. Use a paring knife to make slender holes throughout the non-fat side of the meat that are just wide enough to stuff slivers of garlic into. Put corned beef into the pot fat side down and render over low heat, about 8 minutes. (You don't want it to color.)
Add chopped onions and lightly sauté (don't let them get any color). Add minced garlic. Add a sachet of peppercorns. Cover with water almost to the top of the pot. Bring to a boil then turn down to a simmer and cook for 2 hours. After 2 hours, add the cabbage and cook for 30 more minutes. Then add the carrots and potatoes and simmer for another half hour.
Remove sachet and season to taste. It's best eaten with a healthy dollop of mustard.