Fill a large pot with lightly salted water and bring to a rolling boil. Stir in manicotti and return to a boil. Cook pasta uncovered, stirring occasionally, until tender yet firm to the bite, about 8 minutes. Drain and place on a baking sheet to cool. Place in freezer until hardened, about 5 minutes.
Heat 1 tablespoon oil in a large saute pan over medium-high heat. Add sausage, beef, and onion; saute 3 minutes. Add basil, rosemary, thyme, Italian seasoning, and black pepper. Cook until meat is browned, about 8 minutes. Stir in 1/2 can tomato sauce and cook until heated through, 3 to 5 minutes. Transfer to a large bowl and set aside to cool.
Heat a skillet over medium-high heat for the sauce. Add onion and saute 1 minute. Add remaining tomato sauce, rosemary, and thyme. Stir in basil and red pepper flakes.
Fold mozzarella cheese and cottage cheese into the cooled meat mixture. Stuff each manicotti shell with meat mixture and place back onto the baking sheet. Place filled shells in the freezer to firm up, about 5 minutes. Slice shells into bite-sized pieces.
Heat 2 quarts vegetable oil in a saucepan to 350 degrees F (175 degrees C).
Place flour, bread crumbs, and beaten eggs each in a separate bowl. Dredge manicotti slices in flour, then eggs, and then bread crumbs and place on the baking sheet.
Fry slices in the hot oil until golden brown and crispy, about 5 minutes. Drain on a paper towel-lined plate. Serve with the spicy tomato dipping sauce.