Preheat the oven to 400 degrees F.
Mix the brussels sprouts with olive oil, salt and pepper in a mixing bowl, then transfer to a baking sheet and bake in the oven for about 30 minutes, until starting to brown and tender.
Bring 1/2 cup vegetable broth to boil in a pot and add the black eyed peas. Simmer for 15 minutes, then drain.
Heat a non-stick skillet over medium heat and crack the two eggs. Cover and lower the heat, then cook for about 4 minutes. Sprinkle with salt and pepper.