For the quick tomato sauce: Open the can of tomatoes and pour off the juice into a bowl. Use the lid to press against the tomatoes to extract as much juice as possible. Squeeze the tomatoes to a pulp using your hands. Reserve the juice and pulp separately and set the empty can aside.
Heat the oil in a heavy saucepan over medium-high heat until hot. If using the jalapeno, tilt the pan to collect the oil in a little pool against the side and drop the jalapeno into the oil. Cook until light brown, about 2 minutes. Remove the jalapeno and reserve.
Add the onions to the pan and cook, stirring occasionally, until soft, about 2 minutes. Add the garlic and cook briefly until light gold, and then pour in the tomato juice and bring to a boil. Reduce to a simmer and simmer rapidly for several minutes, and then add the crushed tomato pulp. Rinse the remaining pulp out of the can by filling it halfway with water, and then pour that into the pan. Add the bay leaf, jalapeno, if using, and salt and pepper to taste and return to a boil. Add the dried tomatoes and stir.
Lower the heat to medium and simmer, stirring occasionally to prevent scorching, until the mixture thickens and the tomatoes have turned an orange-red verses the pale blue-red they were straight from the can, about 30 minutes. Add the oregano halfway through the cooking. Discard the bay leaf before using.
For the fusilli: Combine the tomatoes, boiling water, vinegar, sugar and marjoram in a small bowl. Let the tomatoes rehydrate until soft, about 10 minutes. Drain well, squeezing out any excess liquid. Cut the tomatoes into fine julienne slices. Set aside. Discard the marinade.
Bring a large pot of water to a boil. Add some salt and the pasta and cook until al dente, about 10 minutes. Drain, reserving about 1/2 cup of the pasta cooking water.
While the pasta is cooking, heat the olive oil in a large saute pan over medium-high heat until hot. Add the mushrooms and do not move them until they begin to brown, about 1 minute, and then saute until brown all over, about 5 minutes. Season with salt and pepper. Add the garlic and saute briefly until light brown. Add the basil and julienned tomatoes and cook quickly, pulling the pan off the heat as necessary so the tomatoes do not burn.
Add 2 cups of the quick tomato sauce and bring to a simmer. If you chose to add jalapenos to the tomato sauce, seed, mash and reserve them. As soon as the pasta is done, add it to the tomato-mushroom mixture and toss well with 1/2 cup of the cheese and the reserved pasta cooking water. Add 3 cups of the arugula and toss until barely wilted.
Pour into a warm serving bowl or onto a platter and scatter the remaining 1 cup arugula on top. Sprinkle with the nuts and dust with a little cheese. Serve immediately and pass the remaining cheese at the table with a shaker of red pepper flakes, if using, or a small bowl of the mashed jalapenos.
NotesCook's Note: You can substitute 1/2 cup drained, oil-packed dried tomatoes and omit the rehydration step.
This recipe was provided by a chef, restaurant or culinary professional and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.