Prepare split peas. Add rinsed peas to water or broth. Bring to a boil, cover, and reduce heat to a simmer. Cook for 30-40 minutes, or until split peas have softened. Drain from water and let cool slightly.
Preheat oven to 425 degrees Fahrenheit and line a baking tray with parchment paper. Add potatoes and drizzle with avocado oil. Sprinkle with sea salt and pepper. Roast potatoes 30-25 minutes, or until golden and fork tender. Remove from oven and let cool to room temperature.
Prepare pesto: add all pesto ingredients (except for water) to a food processor. Pulse until mixture is incorporated and broken down. If the mixture is too thick, add in a tablespoon or two of water.
Prepare pesto potato salad: in a large bowl combine cooked split peas, potatoes, radishes, spring greens, and pesto. Mix to combine.
Serve potato salad at room temperature, or cover and refrigerate. If refrigerating, don’t add the spring greens until just before serving.