Make the egg mixture. In a medium bowl, whisk together the eggs, grated Pecorino Romano, and grated Parmesan until smooth. Set aside at room temperature.
Sauté the pancetta. Turn on the Instant Pot and select "Sauté" (normal heat). Add the diced pancetta and cook for 4–5 minutes, stirring occasionally, until crispy and the fat has rendered. Use a slotted spoon to transfer the pancetta to a paper-towel-lined plate. Leave the rendered fat in the pot.
Add the garlic. Add minced garlic to the pot and sauté for 30 seconds until fragrant. Press "Cancel" to turn off the sauté function.
Layer the pasta. Break the spaghetti in half and arrange in a crisscross pattern over the rendered fat. Pour in 3 cups of water — just enough to submerge the pasta. Do not stir.
Pressure cook. Close the lid, set the valve to "Sealing," and pressure cook on HIGH for 4 minutes. (Adjust to half the spaghetti package time minus 1 minute if your pasta has a different recommended time.)
Quick release. When the timer ends, carefully perform a quick release by turning the valve to "Venting."
Finish the sauce — critical step. Open the lid. Press "Cancel" and unplug the Instant Pot (or remove the inner pot) so there is no residual heat from the heating element. Immediately pour in the egg-and-cheese mixture and toss vigorously with tongs for 30–60 seconds. The pasta's residual heat will gently cook the eggs into a silky, glossy sauce.
Adjust consistency. If the sauce is too thick, add warm water 1 tablespoon at a time. If too thin, let it sit for 1–2 minutes — it will thicken as it cools.
Stir in pancetta. Add the crispy pancetta back to the pot and toss to combine. Taste and season with salt (if needed) and plenty of freshly cracked black pepper.
Serve immediately. Garnish with chopped parsley and extra grated Pecorino Romano. Serve hot.