Create a two-zone indirect fire in grill by banking charcoal on one side. Alternately, light only half the flames of a gas grill set to high. Stack 2 large pieces of heavy duty aluminum foil and fold edges up to make a cooking tray for fish. Set foil tray over indirect heat on grill. Place fish in foil and season with salt and pepper. Add wine and butter and cover with a flipped over skillet or another sheet of aluminum foil.
Heat nonstick skillet or well-seasoned cast iron skillet on same area of grill. Add oil and beaten eggs to hot pan. Use a rubber spatula to gently scramble eggs in smooth turning motions. Pull pan away from grill just as the eggs set, they will continue to cook. Fold in fresh chives.
Once fish is firm and easy flakes apart when pierced with a fork, remove from grill. Flake fish into bite size pieces and add to eggs. To serve, combine mascarpone, sriracha, and lemon juice in a small bowl. Place eggs and fish on a warm platter, dollop with spicy mascarpone cheese and garnish all around with crispy bagel chips, dill sprigs, and lemon wedges.