Wash and dry all produce. Adjust rack to upper position and preheat oven to 450 degrees. Bring a large pot of salted water to a boil. Line a baking sheet with foil. Roughly chop hazelnuts. Zest lemon until you have 1 tsp zest, then halve. Squeeze 1 TBSP juice into a small bowl. Halve, peel, and finely mince shallot. Mince garlic. Finely chop chives.

In another small bowl, whisk honey, a drizzle of olive oil, and a few large pinches of salt. Place carrots on lined sheet and toss with honey mixture until coated. Arrange carrots toward one side of sheet, keeping at least a quarter of the surface area empty. Roast in oven 12 minutes, then remove from oven and add hazelnuts to empty space on sheet.

Return sheet to oven and continue roasting until carrots are tender and hazelnuts are golden brown, about 3 minutes. Meanwhile, pat chicken dry with a paper towel. Season all over with salt and pepper. Heat a large drizzle of olive oil in a large pan over medium heat. Add chicken. Cook until no longer pink in center, about 6 minutes per side.

Remove chicken from pan, transfer to a cutting board, and cover with foil to keep warm. Melt 2 TBSP plain butter in same pan over medium heat. Add shallot and garlic. Cook until fragrant, 30-60 seconds. Whisk milk and a pinch of salt and pepper into pan, then bring to a simmer. Add Italian cheese, cream cheese, and half the Parmesan. Stir until smooth.

Add pasta to pot of water. Cook until just tender, about 2 minutes. Scoop out 1 cup water, then drain. Return pasta to empty pot off heat. To pan with sauce, whisk in 1/3 cup pasta water. Simmer until just thickened, about 1 minute. Stir in peas and half the chives. Season with salt and pepper. Pour cheese sauce into pot with pasta; stir to combine. TIP: Add more water, 1 TBSP at a time, to loosen sauce, if needed.

Toss carrots with lemon zest and lemon juice. Sprinkle with hazelnuts, if desired. (TIP: Leave them off for picky eaters.) Slice chicken. Divide pasta between plates. Arrange chicken on top and dollop with truffle butter, to taste. Sprinkle with remaining Parmesan and chives. Serve with carrots on the side.