1 1/2 pounds red onions (about 2 large onions)
1 1/2 pounds yellow onions (about 2 large onions)
4 bunches scallions (green part only)
3 tablespoons vegetable oil, such as canola
1 1/2 cups balsamic vinegar
kosher salt to taste
freshly ground black pepper to taste
1/4 cup brown sugar

Peel the onions and cut off the ends, then stand each onion on its bottom and slice it through the center, top to bottom. Continue slicing to produce thin, semicircular julienne strips, then cut those into pieces 2 or 3 inches long. Cut the scallions into pieces 2 or 3 inches long.

Heat the oil in a large skillet over medium heat. Add the onions and scallions and sauté until they begin to soften; cover the pan, lower the heat, and cook until they are wilted, about 20 to 30 minutes. Remove the lid, increase the heat, and add the vinegar. Cook over medium heat, stirring occasionally, until the vinegar is reduced by half. Stir in the salt and pepper, then gradually add the brown sugar, tasting as you go. (Onions have different amounts of natural sugar at different times of the year, so the amount of brown sugar may need to be adjusted. The final flavor should be strongly sweet-and-sour.) Continue cooking the mixture until the jam is thick, about 10 minutes. Remove from heat and cool to room temperature./p>