In a large Dutch oven, heat olive oil over medium-high heat.
Add onion, garlic, and sausage. Cook, stirring frequently, until lightly browned, about 6 minutes.
Add broth and tomatoes; bring to a boil.
Add greens, Conecuh Seasoning, vinegar, salt, and peas. Reduce heat to low; simmer until greens are tender, about 10 minutes.