Recipe courtesy Emeril Lagasse, adapted from Essential Emeril: Favorite Recipes and Hard-Won Wisdom From My Life in the Kitchen, Oxmoor House, 2015, courtesy Martha Stewart Living Omnimedia, Inc.
Pulse the cauliflower florets in a food processor until they resemble coarse crumbs, with some pieces about the size of a pea or slightly smaller. Transfer to a bowl and set aside.
To the food processor (no need to clean out the bowl), add the walnuts, anchovy fillets with their oil, garlic, arugula, parsley, 1/4 cup of the oil, and the red pepper. Pulse until the mixture comes together to form a coarse paste. Add the cheese and lemon zest, and pulse briefly to combine. Set aside.
Bring a large pot of water to a boil and season generously with salt -- it should taste like seawater. Add the spaghetti and cook until it is al dente, usually 8 to 9 minutes. Drain the pasta, reserving 2 cups of the pasta water.
While the pasta is cooking, heat a 14-inch skillet over high heat with the remaining 1/4 cup oil. When the oil is very hot, add the cauliflower and cook, stirring frequently, until it begins to brown around the edges and smells nutty, 5 to 6 minutes. Stir in the arugula pesto and cook briefly, then remove the pan from the heat.
Return the skillet to medium-high heat and add the drained pasta and 1 cup of the reserved pasta water. Using tongs, toss the pasta with the cauliflower and pesto, adding more of the pasta water as necessary to form a sauce that just coats the pasta. Season with salt and pepper to taste, then serve immediately in pasta bowls, garnished with the Toasted Breadcrumbs and additional cheese.