Combine flours on a clean work surface to form a little volcano with a hole in the center. Crack the eggs into the center hole and beat gently with a fork, adding in the chili puree and stirring until eggs and chilies are well combined. Continue to stir the egg mixture with the fork, gradually adding in the flour a little at a time, until the dough becomes too stiff to continue to mix with the fork.
Knead the dough by hand, until it is uniformly smooth, adding in small amounts of flour as needed to prevent it from sticking to your hands and the work surface. If the dough becomes too dry and starts to break apart, sprinkle it with a few drops of water and knead until the dough becomes pliable and smooth. Continue kneading for 10 minutes, or until the dough becomes very velvety and elastic. Cover with a wet towel or plastic wrap and allow it to rest at room temperature for at least 40 minutes.
Meanwhile, while the pasta dough is resting, heat olive oil in a large skillet over medium-low heat. Place the onion slices, whole cloves of garlic and a few leaves of basil in the skillet and cook gently, until the onion is softened but not browned.
Stir in the Mutti® Finely Chopped Tomatoes, reduce heat to low and simmer for about 30 minutes, stirring occasionally. Add colatura di alici, black pepper and salt (keep in mind that the colatura di alici is already salty, so season carefully!). When sauce has finished cooking, remove the onion and garlic. (These are full of flavor. They can be saved to be used in a future recipe.) Keep the sauce covered and warm until ready to serve.
When ready to cook pasta, bring a large pot of salted water to a boil. Cut the pasta dough into quarters. Roll each piece to about ½-inch thick and as wide as the chitarra, keeping the rest of the dough covered while you work to prevent it from drying out. Transfer the rolled-out sheet of dough to the chitarra and gently roll it through the strings to form the spaghetti. Toss with extra durum or semolina flour to prevent sticking and repeat with the remaining pasta dough.
When the water is boiling rapidly, drop the pasta into the water and cook for about 1 minute. Drain and immediately add it to the skillet with the warm sauce. Stir and cook the pasta in the sauce for about a minute, over medium heat, stirring frequently, until it is well combined and nicely thickened. Taste, and if desired, season with additional colatura di alici. Serve with stracciatelli di burrata and garnish with a drizzle of extra-virgin olive oil and additional basil leaves.