Cook the guanciale. Place some paper towels over a plate. Add the guanciale to a large sauté pan. Bring to medium-low heat and cook the guanciale, stirring occasionally, until the fat renders and the lardons turn golden and crisp, 8 to 10 minutes. Transfer the lardons to the paper towels, leaving the rendered fat in the pan.
Cook the pasta. Bring a pot of well-salted water to a boil. Cook the pasta according to the box instructions until just shy of al dente. Before draining, reserve at least 1 cup of pasta water.
Cook the spring onions. While the water comes to a boil, add the white and light green parts of the spring onions to the pan with the guanciale fat. Increase the heat to medium, and season with a pinch of salt and cook, stirring frequently, until completely softened and jammy, about 10 minutes. Add the darker green parts and cook for another 5 minutes, until everything is tender and fragrant. Deglaze the pan with a splash of water (or white wine if you have it), scraping up any browned bits, then stir in the cream. Bring to a simmer and cook until lightly thickened, about 3 to 5 minutes.
Blend the sauce. Transfer the spring onion mixture to a blender with the dill. Blend on high until completely smooth (See Note 3), then slowly stream in the olive oil to emulsify the sauce. It should look glossy and pale green. Season with salt, then strain through a fine-mesh sieve for a silky finish.
Sauté the asparagus. In the same pan used earlier, melt the butter over medium-high heat. Add the asparagus and cook, tossing occasionally, until bright green and just tender with a slight bite, 2 to 3 minutes.
Bring it all together. Transfer the pasta directly into the pan with the sauce, along with about ½ cup of reserved pasta water. Increase the heat to medium-high and stir vigorously until the sauce thickens and clings to the noodles. If the sauce looks too thick or tight, add more pasta water a splash at a time until it becomes glossy and coats the pasta.
Finish and serve. Remove from the heat and fold in the Parmesan and crispy guanciale. Taste and adjust with salt and pepper. Serve immediately, topped with more Parmesan, fresh dill, and a squeeze of lemon juice if using.
