Heat 2 tablespoons olive oil in a large skillet over high heat. Add half the green beans and season generously with salt and pepper. Cook, undisturbed, until starting to brown, about 3 minutes. Toss and continue cooking until tender, 3 to 4 minutes; transfer to a rimmed baking sheet. Add another 2 tablespoons olive oil to the skillet and repeat with the remaining green beans; add to the baking sheet and wipe out the skillet.
Add the remaining 2 tablespoons oil and the sausage to the skillet. Cook over medium-high heat, breaking up the meat, until lightly browned, 4 to 5 minutes. Remove with a slotted spoon to the baking sheet with the green beans. Add the red onion, fennel and thyme to the skillet, season with salt and cook, stirring, until softened, 4 to 5 minutes.
Return the beans and sausage to the skillet and toss; season with salt and pepper. Transfer to a serving dish and top with fennel fronds.
Cook the whole dish up to 4 hours ahead; cover and refrigerate. Reheat in a 300 degrees F oven; top with fennel fronds before serving.