Set the Instant Pot to Sauté and add the olive oil.
Add the onion, celery, and carrots. Season lightly with salt and pepper and sauté for 4–5 minutes, stirring occasionally, until the onions are translucent.
Add the spices, garlic, and tomato paste. Stir well and cook for 2–3 minutes, until fragrant and the tomato paste deepens in color.
Pour in the white wine and cook for 1–2 minutes, until mostly evaporated. Turn off the Instant Pot.
Add the zucchini, diced tomatoes, vegetable broth, bay leaves, parsley, water, and beans, and Parmesan rind, if using. Stir well.
Secure the lid and set the pressure valve to the Sealing position. Select Pressure Cook (High Pressure) and set the timer for 6 minutes.
When the cooking time is complete, carefully perform a quick pressure release, keeping your hands and face away from the escaping steam.
Once the pressure has fully released, remove the lid and discard the bay leaves and Parmesan rind.
Select Sauté and add the kale and cubetti pasta. Cook for 12 minutes, stirring occasionally, until the pasta is tender and the kale is cooked through.
Turn off the Instant Pot. Stir in the pesto, apple cider vinegar, and 1 teaspoon of salt, or more to taste. Season with additional black pepper as needed.
Serve hot with grated vegetarian-friendly Parmesan-style cheese, if desired.