Season cod with salt and pepper. Spread pesto over fish fillets and set aside.
Lay out 1 large sheet (about 16" x 12") of parchment paper. Place potato slices, asparagus, tomatoes in the center of the paper, season with salt and pepper, a splash of lemon juice. Place fish fillet on top with a slice of lemon. Drizzle 1 tablespoon extra-virgin olive oil, and 2 sprigs of thyme.
Fold over the ends of the paper to enclose the fish. Place on a baking sheet. Repeat with remaining fish.
Bake for about 15-20 minutes, or until fish reaches 130˚F to 135˚F on a thermometer.
