Preheat oven to 350°. Bring a large pot of salted water to boil over high heat. Boil pasta per package directions for al dente. Drain and return to pot.
While waiting for pasta to cook, combine breadcrumbs, parmesan cheese, oregano, and ¼ tsp salt and pepper in a small shallow bowl. Set aside.
Heat canola oil in a large skillet (preferably cast iron) over medium-high heat. Add eggplant to a medium bowl. Toss with flour to coat, then toss with egg to coat.
When oil shimmers, dredge eggplant pieces in breadcrumb mixture and then place in the skillet. Fry for 3-5 minutes, turning occasionally, until golden brown. Remove to a paper towel lined plate. Remove heat.
Pour off all but about 2 tbsp oil from the skillet. Return to medium heat. Add garlic and cook briefly until fragrant. Add tomatoes and bring to a simmer. Stir in thyme, red pepper flakes, and ½ tsp salt.
Add pasta and eggplant to the skillet and mix to combine. Cover with mozzarella cheese. Bake for 30 minutes or until cheese is bubbly and eggplant is tender.