1

Heat a very large skillet over high heat. Put the onions in the skillet and spray them with olive-oil nonstick spray. Stirring almost constantly, cook until dry and just turning light golden, about 25 minutes. Stir in the brown sugar and vinegar and cook until the onions are dark golden and reduced in volume by two-thirds, about 5 minutes longer. Transfer onions to a bowl and stir in the pepper.

2

Preheat oven to 375°F. Combine the spinach, garlic, oil, and water in a food processor and process until smooth.

3

Fit half of a phyllo sheet snugly into a 7 x 11-inch baking dish, with the other half hanging over the edge. Spray with olive-oil nonstick spray and sprinkle with 1/2 teaspoon of the thyme. Fold the other half of the phyllo over into the pan, spray it, and sprinkle with another 1/2 teaspoon thyme. Repeat process with the 3 remaining phyllo sheets to make an 8-layer crust, omitting the sprinkle of thyme on the top. Spread the spinach pesto over the crust, sprinkle with the cheese, and spread onions to cover top to the outer edges. Bake until browned on top, about 20 minutes. Remove from oven, let stand 5 minutes, then cut into 8 squares.