Melt the butter and olive oil in a heavy-bottomed pot over medium heat. Add the onions, thyme, bay leaf, garlic, salt, and a few grinds of pepper. Cover and cook over medium-low heat until very soft, about 20 minutes.
Uncover, add the vinegar and sugar, and cook, stirring frequently, until thickened, 20 minutes or longer. Remove the bay leaf.
Transfer jam to a bowl and let cool. Taste and season with more salt and pepper as needed.
