Heat an outdoor grill or a grill pan over medium-high.
Season the fish on both sides with salt and pepper. Douse with the vermouth and coat in EVOO. Season the cut sides of the lemons and drizzle with EVOO.
For the peperonata, roast the red peppers over a gas burner or under the broiler, turning occasionally, until blistered and blackened all over. Transfer the peppers to a large bowl, cover with plastic wrap and let steam 15 minutes. Using a paper towel, rub the skin off the peppers, then split, seed and remove the stems. Slice lengthwise into 1/4-inch-thick strips, then cut the strips in half crosswise.
While the peppers are steaming, in a large skillet, heat the EVOO, four turns of the pan, over medium. When the oil shimmers, add the onions, cubanelle, chile, garlic and oregano; season. Partially cover and cook, stirring occasionally, until vegetables soften, 4 to 5 minutes. Add the tomato paste and stir 1 minute. Stir in the vermouth and sugar. Add the stock, capers, vinegar and the roasted red peppers. Reduce the heat to low and let simmer while you cook the fish, about 10 minutes.
Grill the fish and the lemons, cut side down, until the fish is just opaque in the center, 3 to 4 minutes per side, and the lemons are charred in spots, about 4 minutes.
Douse each halibut steak with the juice of half a lemon and top with lots of peperonata. Garnish with the parsley and toasted almonds, if desired.