Preheat the Instant Pot on the Saute function set to 10 minutes. Add the olive oil and sauté the minced garlic and shallot for 5 minutes, or until fragrant and translucent.
Add the anchovy fillets to the pot, gently mashing and incorporating with the garlic and shallot. Cook for an additional 2-3 minutes, until fragrant.
Add capers, olives, whole tomatoes, oregano, red pepper flakes, black pepper, and salt. Stir to combine.
Gently break the bucatini so all the pasta fits horizontally in the pot. Add the chicken stock and gently stir to combine.
Press Cancel and cook the pasta on High for 10 minutes. Allow the Instant Pot to naturally release for 5 minutes before flipping the valve and releasing the remaining pressure.
Stir in the raw halved tomatoes, Parmesan, basil and parsley. Sprinkle with additional Parmesan as desired.