Heat a large 12-inch skillet over medium-high for at least 2 minutes.

Drain the corned beef package into the sink — do not rinse. Save any spice packet that came with the meat if present.

Add 2 tablespoons of oil to the hot pan; when it shimmers, add the drained corned beef fat-side down and sear for 2–4 minutes until golden. Flip and sear the other side for 2–3 minutes.

Transfer the seared brisket to the crock pot fat-side up. Keep the skillet for deglazing.

In a measuring cup, whisk together beef broth and whole grain mustard. Pour this into the hot skillet, stirring over medium-high heat while scraping up browned bits until the liquid simmers.

Pour the deglazed mixture over the brisket in the crock pot.

Smash the garlic cloves with the flat of a knife and add them to the pot with the onion, peppercorns, thyme sprigs, bay leaves, and the saved spice packet.

Cover and cook on LOW for 6–7 hours.

Meanwhile, peel the carrots and cut them into thirds. After the initial cooking time, add the carrots on top of the brisket, replace the lid, and cook on LOW for another 1–2 hours until the carrots are tender.

While the carrots cook, melt butter in the skillet. Add the cabbage and sprinkle with kosher salt. Sauté for about 10 minutes until slightly wilted.

Nest the sautéed cabbage on top of the carrots in the crock pot and continue cooking on LOW for another 30–60 minutes.

Preheat the oven to 425°F (220°C). Cut red potatoes into 1-inch pieces, toss with oil, salt, pepper, and optional herbs. Spread on a baking sheet and roast for 25–35 minutes until golden and crisp.

Transfer cabbage to a colander to drain slightly, gather carrots on a serving platter, and place cabbage next to them.

Transfer the brisket to a cutting board, let rest for 10 minutes, slice against the grain, and arrange on the platter.

Add roasted potatoes, garnish with parsley and chives, and serve with horseradish sauce and Irish soda bread.