Combine the balsamic vinegar and honey in a 1-quart saucepan over medium heat. Simmer for 6 to 8 minutes, stirring occasionally, until reduced by half and thick enough to coat the back of a spoon. Set aside to cool; it thickens further as it sits.

Heat an outdoor grill or 11-inch square grill pan to medium-high, about 400 F / 205 C. Brush the grates with 1 tbsp of the olive oil.

Salt the eggplant rounds and let them sit for 10 minutes, then pat dry with a paper towel. This pulls out excess moisture so they char instead of steam.

Toss the zucchini, eggplant, bell pepper, and onion rounds in a mixing bowl with the remaining 3 tbsp olive oil, garlic, oregano, salt, and black pepper.

Grill the vegetables in batches so the pan isn't crowded. Cook zucchini and eggplant for 3 to 4 minutes per side, bell pepper for 4 to 5 minutes per side, and onion rounds for 3 minutes per side, until all pieces are grill-marked and tender. Transfer to a platter and let cool for 5 minutes.

Slice the chilled goat cheese log into 8 rounds using a knife dipped in warm water, wiping the blade clean between cuts.

On each of 4 plates, layer 1 piece of bell pepper, 1 goat cheese round, 2 zucchini planks folded in half, a few onion rings, and 2 eggplant rounds, then top with a second goat cheese round.

Drizzle each stack with the cooled balsamic glaze, scatter torn basil and toasted pine nuts over the top, and serve right away while the vegetables are still warm.