Preheat the oven to 350°F.

Lay 4 pieces of aluminum foil on the counter, each approximately 14 x 12 inches. Distribute the carrot, zucchini, and yellow squash matchsticks near the centers of each piece of foil. Scatter the sliced mushrooms and garlic over the vegetables. Generously season with salt and pepper.

Season each snapper fillet with salt and pepper and put one on top of each pile of vegetables. Place 3 slices of tomato on each fillet.

Drizzle each portion with 2 tablespoons olive oil and sprinkle with thyme.

Bring the 2 longer sides of the foil together over the fish and seal the edges by folding them over, as you would wrap a sandwich or fold a letter. Tuck the sides in, folding them together once or twice to form an airtight seal. Make sure there is some room for air to circulate in the packets and that they’re not bursting at the seams. Transfer the packets to 2 baking pans large enough to hold them in a single layer or a rimmed baking sheet and bake for about 25 minutes, or until the fish is cooked through and the vegetables are tender. Check one packet by unwrapping it very carefully; the escaping steam will be hot.

Put a packet on each plate and warn everyone to open them with great care because the steam is very hot. Or, open them before serving, transferring the contents to individual shallow bowls or a serving platter.