Saute the onion and celery in olive oil (2 tablespoons) in a large pot until tender (approximately 3 minutes).
Add garlic, sauté for 30 seconds more, or until fragrant.
Add vegetable broth (8 cups), split peas, and diced potatoes to the pot and stir. Season with salt and pepper.
Bring to a boil. Cover and simmer on low for 1-1.5 hours, or until split peas are tender. If soup gets too thick, add more broth.
Turn off heat. Stir in fresh dill (1/4 cup) and lemon juice (2-4 tablespoons, depending on how lemony you want it), stir.
Taste and adjust seasoning as necessary. If soup seems too thick, more water or vegetable broth can be added. Serve with an extra drizzle of olive oil and a squeeze of fresh lemon juice, if you want.
If using a potato with a thin skin, like gold or red, you can leave the skin on. But for a thicker skin, like russets, I recommend peeling them.
Freezer storage: This soup can be frozen in an airtight container for up to 6 months.
Instant pot directions: Sauté the onion and celery in the olive oil using the sauté function. Add the garlic, sauté for 30 seconds, then add the broth, split peas, and potatoes. Season with salt and pepper. Cook on high pressure for 10 minutes. Naturally release the pressure for 10 minutes, then quick release and wait for the float valve to depress before opening. Stir in the lemon juice and dill, season to taste.
Slow cooker directions: Add everything except for the lemon juice and dill to your slow cooker. Cook on high for 4 hours or low for 8 hours. Stir in the lemon juice and dill after it's done cooking and adjust seasoning if necessary.