Brush bread with 1/4 cup of the olive oil and season with 1/4 teaspoon salt and 1/2 teaspoon freshly ground black pepper. Arrange on a baking sheet and bake until golden, about 10 minutes.

Meanwhile, heat the remaining 1/4 cup plus 2 tablespoons of oil in a skillet. Add onions and cook, stirring occasionally, until soft and tender, about 8 minutes. Add vinegar and cook until it evaporates, about 30 seconds. Season with remaining 1/4 teaspoon salt and 1/4 teaspoon freshly ground black pepper. Cool to room temperature. Divide onions evenly among crostini and top each with about 1 teaspoon crumbled cheese. Garnish each crostini with 1/4 teaspoon of chives and serve immediately at room temperature.