Rinse the buckwheat groats under cold water and set aside.
Set the Instant Pot to the 'Sauté' function and add olive oil.
Once the oil is hot, add the diced onion and sauté for 2-3 minutes until translucent.
Add minced garlic and sauté for an additional minute, making sure not to burn it.
Incorporate the diced carrot and zucchini, and continue to sauté for another 3-4 minutes until slightly softened.
Stir in the chopped kale or spinach, diced tomatoes (with their juices), vegetable broth, oregano, basil, and the rinsed buckwheat groats.
Season with salt and pepper to taste, and give it a big stir to combine all ingredients.
Close the lid of the Instant Pot, ensuring the valve is sealed. Set it to 'Manual' or 'Pressure Cook' on high for 10 minutes.
Once cooking is complete, allow for a natural release for about 10 minutes before manually releasing any remaining pressure.
Open the lid carefully, stir the minestra, and adjust seasoning if needed.
Serve hot with grated Parmesan cheese on top if desired.