Pre-heat oven to 200 degrees F. Slice tops of Romas off and then cut in half lengthwise. Mix in a bowl with sugar and salt. Place on a sheet pan cut-side up and bake for 2 1/2 hours. Turn oven off and leave tomatoes inside overnight. The next day turn the oven on to 200 degrees F. and slow roast the tomatoes for 5 to 7 more hours, depending on size. The tomatoes should be shriveled, but not at all crispy. Remove from oven, let cool, and then cut into julienne strips. Pre-heat oven to 300 degrees F. Place whole garlic cloves and 1/4 cup olive oil in an aluminum foil packet and bake for 2 1/2 hours. Cloves should be very soft. Place cloves in blender or food processor and puree to a smooth paste, scraping down sides occasionally. Julienne one large head of fennel, toss with 1 tablespoon oil, a pinch of salt and freshly ground pepper, and roast in oven for 2 hours.
Dice remaining fennel, put in a saucepan, just cover with water, and simmer until very soft. Puree in a blender. Allow to cool slightly and squeeze liquids out through a cheesecloth, reserving liquid. Discard solids. Cook pasta in 2 quarts rapidly boiling salted water, drain and set aside. Heat remaining oil in a skillet, add slivered garlic and stir until golden brown. Add broccoli rabe, saute to warm it, add crushed red pepper and oregano (if using dry). Add fennel juice and reduce by half. Add roasted fennel, oven-dried tomatoes, garlic puree, and oregano (if using fresh). Stir in pasta. Serve in shallow bowls and garnish with shaved Parmesan cheese.