Heat 2 tablespoon of the olive oil in a large, heavy-bottomed pot over medium-high heat. Add half of the mushrooms and cook them in a single layer until the edges are brown and starting to crisp (about 3 minutes). Don't mess with them during this time. Let them cook undisturbed.

While the mushrooms are cooking, cook the bucatini in a large pot of salted water according to package directions. Toward the end of the cook time, reserve 1 cup of pasta water.

Toss the mushrooms and continue to cook them, tossing occasionally, until they are brown and crisp on all sides (3-5 additional minutes).

Transfer the crispy mushrooms to a plate using a slotted spoon and then season them with kosher salt. Repeat steps 1-3 with the remaining 2 tablespoon of oil, mushrooms, and salt.

Reduce the heat to medium-low and return all of the mushrooms to the pot. Add the shallot and garlic to the pot and cook, stirring often, until the shallot is translucent and softened and the garlic is fragrant (about 2 minutes).

Strain the pasta and add it to the pot with the mushrooms and add half and half and 1 cup of the pasta water. Turn the heat up to medium and bring everything o a simmer. Cook the pasta, tossing constantly, until the liquid has thickened slightly (about 3 minutes).

Remove the pot from heat. Add the lemon zest and juice, chives, butter, shredded parmesan cheese, and kosher salt and pepper, to taste, and toss everything to combine. Taste and season again, if needed.

Divide the pasta among plates or bowls and top with more chives and parmesan cheese, if desired.