Heat the olive oil in a large high-sided saute pan over medium-high heat. Add the soppressata and cook until lightly browned around the edges, 3 to 5 minutes. Use a slotted spoon to transfer the soppressata to a paper-towel-lined plate. Add the fennel to the pan and cook until just softened and lightly browned, 4 to 6 minutes. Add the browned soppressata, tomatoes, jalapeno juice, pickled jalapenos and 2 cups water. Cook until the liquid has reduced by almost half and the tomatoes just start to soften, about 5 minutes. Stir in the butter. Turn off the heat and cover with a lid.
Heat 2 tablespoons of the vegetable oil in a large nonstick saute pan over medium-high to high heat. Sprinkle the halibut liberally with salt and pepper. When the oil just starts to smoke, gently place 2 of the fillets in the pan and sear until browned on both sides, about 5 minutes total. Transfer to a large plate. Sear the remaining fillets, using the remaining vegetable oil if needed.
To serve, divide the soppressata mixture and broth evenly among 4 shallow bowls. Top with the halibut, a drizzle of olive oil and garnish with the reserved fennel fronds. Serve with crusty bread if desired.