In a medium saute pan, heat the oil until it begins to smoke lightly. Add the onions and season with salt and pepper, to taste. Cook until the onions give up their liquid, 3 to 5 minutes, and then add the red wine. Lower the heat and cook the onions until the wine reduces almost completely. Leave on low heat while you prepare the gastrique.
In a separate small pan, heat the honey until it begins to bubble and froth. Cook until the honey turns a light caramel color, an additional 2 to 3 minutes. Add the red wine vinegar, simmer for a few minutes on low heat, and then shut off the heat. Pour the honey mixture over the onions and continue cooking them over low heat until all of the juice is absorbed and the onions are a jam-like consistency, 10 to 15 minutes. If you desire, add lemon juice and zest at this point. Taste for seasoning and transfer to a bowl to cool until ready to serve.
Recipe courtesy Alex Guarnaschelli