Heat oil in heavy large pot over high heat. Add onions and cook until soft and beginning to brown, stirring frequently, about 8 minutes. Reduce heat to medium-high. Add mushrooms and sauté until wilted, about 3 minutes. Add peppers and sauté until just soft, about 5 minutes longer.
Meanwhile, cook pasta in large pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain, reserving 1 cup cooking liquid.
Add reserved pasta cooking liquid and 2 teaspoons marjoram to skillet and stir, scraping up browned bits. Add drained pasta to sauce and toss to coat. Add 1 cup cheese; stir until melted. Transfer pasta to large bowl; sprinkle with remaining 1/2 cup cheese and 1 teaspoon marjoram.