Cook the pasta: Bring a large pot of well-salted water to a rolling boil. Add 80g pasta and cook until just al dente according to packet instructions. Before draining, scoop out at least 1 cup of pasta water and set aside in a heatproof mug. Drain the pasta and set aside.
Prepare the egg and parmesan mixture: While the pasta cooks, whisk together 1 egg yolk and 1 whole egg in a medium bowl until fully combined with no streaks of white remaining. Add 1/4 cup finely grated parmesan cheese and whisk until smooth and fully incorporated.
Sauté the garlic and spring onion: Heat 1 1/2 tbsp extra virgin olive oil and 1 tbsp chilli oil together in a large wide pan over medium heat. Once shimmering, add 1 tbsp thinly sliced garlic and 1 tbsp finely chopped spring onion. Reduce to medium-low and sauté, stirring frequently, until fragrant. Do not let the garlic brown or burn.
Combine the pasta and egg mixture: Remove the pan from the heat completely or turn to the lowest setting. Add the cooked pasta and pour the egg and parmesan mixture over the pasta. Toss continuously and vigorously with tongs, adding pasta water in small splashes of 2–3 tbsp at a time, tossing between each addition, until the sauce is silky, glossy, and coats the pasta beautifully. Taste and add salt if needed.
Plate and finish: Twirl the pasta into a bowl using tongs to form a high, neat mound. Spoon over any remaining sauce from the pan. Drizzle generously with extra chilli oil and scatter over extra parmesan if desired. Serve immediately.