Preheat oven to 375°F.
Rinse the split peas in a colander, picking through them and discarding any rocks or funky looking peas. Transfer them to a small pot and add just enough water to cover them. Bring the water to a lively simmer, then reduce the heat to low. Continue to simmer the split peas for about 20 minutes until they are tender, but still have a bite.
While the split peas are cooking, chop the butternut squash into bite-sized cubes (if it isn’t already). In a large oven-safe skillet, heat 1 tbsp olive oil over medium heat. Add cubed butternut squash and cook, stirring occasionally, until slightly browned and on its way to tender, about 10 minutes.
Add diced onion, turmeric, salt, and pepper (and more olive oil if needed) and continue to cook for 5 minutes, until the onions begin to soften.
Toss in the chopped kale and a splash of tomato liquid from the canned tomatoes. Cook for a few minutes until kale wilts slightly, stirring and scraping up any caramelized bits from the bottom of the pan as it cooks.
At this point, your split peas should be ready. Add the drained split peas and chopped tomatoes with their juices to the pan. Add a bit more salt and pepper, stir the mixture to combine, and continue to cook for about 5 minutes. The butternut squash should be fork-tender and the mixture should be slightly thickened.
Turn off the heat. Crumble the goat cheese into the pan. Use the back of a wooden spoon to create 4 or 5 indentations in your giant veggie mixture and crack an egg into each one.
Transfer the pan to the oven and bake until eggs whites are just set, 8-10 minutes. The egg whites may look a bit jiggly when you remove the pan from the oven, but they will continue to cook and solidify as you plate up.
Brunch is served, hopefully with crusty bread on the side!