For this comforting soup, Alex Guarnaschelli cooks fresh and canned tomatoes separately, which adds layers of flavor. She then purees some of the soup and leaves the rest chunky to give it a lovely texture. Slideshow: More Warming Soup Recipes
In a large cast-iron skillet, heat the canola oil until nearly smoking. Add the plum tomatoes and sugar and season with salt. Cook over moderately high heat, turning, until the tomatoes are lightly charred and starting to burst, about 10 minutes. Add the Pernod and cook over moderately low heat, breaking up the tomatoes, until a chunky sauce forms, about 20 minutes.
In a saucepan, heat 1/4 cup of the olive oil. Add the fennel, shallots, garlic, fennel seeds, oregano, crushed red pepper and a generous pinch each of salt and white pepper. Cook over moderate heat, stirring, until the fennel starts to soften, 5 minutes. Add the canned tomatoes with their juices and 4 cups of water and bring to a boil. Simmer over moderately low heat, stirring, until the fennel is very tender, 20 to 25 minutes.
Ladle half of the fennel mixture into a blender and puree until nearly smooth; return the puree to the saucepan. Transfer the chunky tomato sauce to the blender and puree until smooth. With the machine on, gradually add the remaining 1/2 cup of olive oil until incorporated. Stir the tomato sauce into the saucepan along with the vinegar. Cook over moderately low heat until heated through and season with salt and white pepper. Garnish with fennel fronds and serve, passing shaved cheese at the table.