Bring 6 quarts water to boil in a large spaghetti pot and add 2 tablespoons salt.
Clean soft shell crabs by snipping off their faces with a pair of scissors and removing the skirt. Cut in half and set aside.
In a 12 to 14-inch saute pan, heat olive oil until smoking, add onions, Anaheim, jalapenos and cook until softened, about 8 to 10 minutes. Add the crab pieces and continue cooking until crabs are deep red and firm. Be careful not to break up the crabs with aggressive stirring. Add the white wine and the tomato sauce and reduce by half. Add escarole and cook another 1 minute until escarole has wilted and remove from heat. Drop fusilli into boiling water and cook according to package instructions until al dente (about 7 to 9 minutes). Drain pasta well in colander and pour hot pasta in pan with crabs. Return to medium heat and toss to coat well, about 1 minute. Pour into heated serving platter and serve immediately.
Saute the onion and garlic in the olive oil over medium heat until translucent, but not brown (about 10 minutes). Add the thyme and carrot and cook 5 minutes more. Add the tomatoes. Bring to a boil, lower the heat to just bubbling, stirring occasionally for 30 minutes. Season with salt to taste. Serve immediately, or set aside for further use. The sauce may be refrigerated for up to one week or frozen for up to 6 months.