Remove the stalks and fronds from each fennel bulb, saving a few fronds. Slice the bulb into paper-thin rounds with a mandoline or knife. Discard the root end of the bulb.
Cut four 2-foot-long pieces of parchment paper. Place on a clean work surface and divide the sliced fennel between the parchment paper, making a small pile of fennel in the center of each piece.
Place one salmon fillet on top of each pile of fennel. Top each piece of salmon with two thyme sprigs and 1–2 fennel fronds. Sprinkle the orange zest over the salmon, dividing it evenly between the four fillets. Sprinkle each fillet lightly with kosher salt.
Fold the two long ends of parchment together so they meet above the salmon, then roll and pinch together to seal the edges. Do the same to the short edges of parchment paper to make a packet.
Place the four packets on two large baking sheets. Roast for 12–15 minutes, then carefully transfer each packet to a serving plate. Carefully open each packet and drizzle Carapelli Oro Verde Extra Virgin Olive Oil on the cooked salmon and sprinkle with fresh thyme leaves. Serve immediately.