Step 1

In a large stainless steel skillet or medium Dutch oven, heat rendered pork fat (or olive oil) over medium-high heat until shimmering. Add onion, fennel, and celery, season lightly with salt and pepper, and cook, stirring occasionally, until vegetables are softened and just beginning to brown, about 8 minutes. Add garlic and rosemary (if using), and cook, stirring frequently, until fragrant, about 30 seconds. Add wine and cook, swirling pan and scraping up any stuck-on bits with a wooden spoon, until wine is reduced by a third, about 30 seconds.

Step 2

Add stock, season lightly with salt, and bring to a boil. Add the pork and pork drippings (if using), reduce heat to a gentle simmer, partially cover and cook, stirring occasionally, until pork is fully tender and easily shreds apart when pressed with a wooden spoon, and liquid is reduced to a saucy consistency, about 1 hour.

Step 3

Meanwhile, in a pot of salted boiling water, cook pasta. If using fresh pasta, cook until noodles are barely cooked through. If using dry pasta, cook until just shy of al dente (1 to 2 minutes less than the package directs). Using either tongs (for long fresh pasta) or a spider skimmer (for short pasta), transfer pasta to pan along with 1/2 cup (120ml) pasta cooking water. Alternatively, drain pasta using a colander or fine-mesh strainer, making sure to reserve at least 2 cups (500ml) pasta cooking water.

Step 4

Increase heat to medium-high and cook, stirring and tossing rapidly, until pasta is al dente and sauce is thickened and coats noodles, about 1 minute, adding more pasta cooking water in 1/4 cup (60ml) increments as needed. Add the butter and stir and toss rapidly to melt and emulsify into the sauce. Remove from heat, add lemon juice and zest, and 3/4 of grated cheese, and stir rapidly to incorporate. Season with salt to taste. Divide pasta between individual serving bowls, garnish with reserved fennel fronds, and sprinkle with remaining grated cheese. Serve immediately.