In a mini food processor, pulse the chives and tarragon leaves until chopped. Add the butter and a pinch each of salt and white pepper and pulse just until the butter is bright green with flecks of herbs. Transfer the herb butter to a sheet of plastic wrap and form into a log. Freeze for about 5 minutes, until the butter is slightly firm. Cut the butter into 16 pieces.
Arrange four 12-inch sheets of heavy-duty foil on a work surface and spray evenly with vegetable oil spray. In a medium bowl, toss the corn with the shiitake and season with salt and pepper. Mound the mixture in the center of the foil sheets and top each mound with a piece of the herb butter. Top with the halibut fillets and another piece of the herb butter and season with salt and pepper. Fold up the foil on all sides and pinch the seams to seal.
Light a grill. Place the foil packets on the grill, close the lid and cook over high heat until the fish is cooked through and the mushrooms are tender, 8 to 10 minutes; let the packets rest for 2 minutes.
Grill the baguette slices for 2 minutes, turning once. Top with the remaining herb butter, allowing it to melt. Open the packets and serve the fish and vegetables with the baguette toasts.