In pot, cook pasta in boiling salted water until al dente; drain, reserving 1/2 cup pasta cooking water. Meanwhile, in skillet, heat oil over medium-high. Add pastrami. Cook, stirring often, until browned, 2 to 3 minutes. Scrape pastrami into large bowl; let cool. Whisk in eggs and yolks, 5 tbsp. parsley, and garlic. Whisk in 3/4 cup Parmesan. Gradually whisk in hot pasta cooking water. Toss pasta with sauce; season. Garnish with parsley and Parmesan.