Step 1

Bring a large pot of water to a boil.

Step 2

Add 1/4 cup olive oil and chili paste or flakes to a large, heavy-bottomed skillet set over medium heat. Once hot, add breadcrumbs, season with salt to taste and cook, stirring occasionally, until toasted, about 3 minutes. Remove from heat and set aside on a paper towel-lined plate.

Step 3

Meanwhile, in a food processor, pulse carrots until finely chopped. Transfer to bowl and rinse and wipe out the food-processor bowl. Add the onion and pulse until finely chopped. Transfer to a separate bowl and wipe out the food-processor bowl. Working in batches, pulse the cauliflower in the food processor until it is riced. Transfer to a separate medium bowl. Repeat with remaining cauliflower.

Step 4

Wipe out the skillet and add 1/4 cup olive oil and 3 tablespoons butter over medium heat. Add the carrot and cook, stirring occasionally, until starting to soften, about 5 minutes. Add onion and cook, stirring occasionally, until softened and translucent, 10 to 12 minutes. Add in garlic, anchovies, and nutmeg and cook for 3 to 5 minutes until the anchovies have melted into the mixture. Add in the tomato paste, and cook, stirring constantly, until the paste has darkened in color, 3 to 4 minutes.

Step 5

Add in the cauliflower and cook, stirring occasionally, for 10 minutes, or until the cauliflower starts to break down, caramelize, and hug the bottom of the pan. Adjust seasoning to taste and reduce the heat to low.

Step 6

Meanwhile, cook the pasta 1 minute shy of the package instructions. Reserve 1½ cups pasta water and drain. Add the pasta to the pot along with zest of 1 lemon, reserved butter and 1/2 cup of reserved pasta water. Toss to combine, slowly adding in 1/4 cup of Parmesan cheese. Alternate between pasta water and cheese until the pasta is coated and the sauce looks glossy. Add more salt to taste. Squeeze lemon over the pasta and toss one more time.

Step 7

Divide the pasta among serving bowls and top with spicy breadcrumbs, basil, remaining Parmesan and a drizzle of olive oil.