Sauté the vegetables and spices. Press the "sauté" setting on the Instant Pot and heat the oil. Add the onion, carrots, and celery, and sauté until softened but not browned, for 3-5 minutes. Add the garlic and smoked paprika and sauté until fragrant, for about a minute. Then, press “cancel” on the Instant Pot.
Simmer. Add the split peas, thyme, bay leaf, vegetable broth, and water, and season with salt (if the vegetable broth doesn't contain salt already). Secure the lid and set the steam release knob to the "sealing" position. Press the "pressure cook"/"manual" mode, and set it to high pressure for 15 minutes.
Release the pressure. Once the cooking time is up, let the pot sit undisturbed for 15 minutes to release some of the pressure. Then, turn the steam release knob to "venting" to quick release the remaining pressure.
Stir in the lemon juice.
Season. Taste and adjust the flavor, adding more salt for saltiness, garlic for pungency, smoked paprika for smokiness, and lemon juice for acidity. Remove the thyme stems and the bay leaf before serving.
Purée (optional). Completely smooth or a little chunky is a personal preference. I like the peas to be soft, almost disintegrated, but still with some texture. My husband prefers silky smooth split pea soup. To purée the soup, use an immersion blender or a countertop blender.
Serve. Garnish the soup with finely chopped fresh parsley and cracked black pepper. Serve hot.
Store. Leftover split pea soup keeps well covered in the refrigerator for 3-4 days. For longer-term storage, freeze in an airtight container for up to 3 months.
Reheat. The easiest way to reheat frozen soup is to remove it from the freezer and place it in the refrigerator 24 hours before reheating to thaw slightly. When ready to reheat the soup, pour it into the Instant Pot. Secure the lid and set the steam release knob to the "sealing" position. Press the "pressure cook"/"manual", and set it to "0". When the timer beeps, the Instant Pot will automatically switch to “keep warm” mode and will keep the soup hot.