Cover potatoes and carrots with well-salted water in a small pot. Bring to a boil over medium-high heat, then reduce heat and simmer for about 20 minutes, or until potatoes and carrots are fork-tender. Drain and reserve about 1 cup of cooking water.

To make the shiitake crisps, preheat oven to 375ºF and line a baking tray with parchment paper. Place the sliced shiitake in a mound on the lined tray. Drizzle with olive oil. Toss to coat then arrange in a single layer on the pan. Sprinkle with salt. Roast for 20 to 25 minutes until they almost look burnt. Remove them from the oven. Set aside to cool and crisp up.

Meanwhile, melt 4 tablespoons of butter in a large pan over medium heat. Add the leeks, Brussels sprouts, garlic, salt, and pepper. Cook, stirring frequently, until soft, about 10 minutes. Add milk and bring to a simmer. Transfer drained potatoes and carrots to the pan and mash with a potato masher or fork. Add a little of the reserved cooking water to thin, if necessary. Season with more salt and pepper, if desired, but remember the cooking water, if used to thin has salt in it.

Transfer colcannon to a large serving bowl. Make a divot in the top and place the remaining 2 tablespoons of butter in it. Garnish with scallions and shiitake crisps.