Pour the olive oil into a large saucepan over medium-low heat. When hot, add the onion and sugar. Cook, stirring occasionally, until the onions are extremely soft, golden brown and caramelized, about 40 minutes. If the onions start to burn when cooking, lower the heat. Once cooked, stir in 2 cups of the vegetable broth, scraping up any flavorful bits that are stuck to the pan. Set the onion and broth mixture aside and allow to cool to room temperature. When cool, pour the onion mixture into the pitcher of a blender or a food processor fitted with the s-blade, or use an immersion blender. Puree until smooth. Set aside.

Set the same saucepan back on the burner, this time over medium heat. Add the butter and heat until melted. Stir in the flour, salt and pepper. Cook, stirring constantly, for three minutes. Stir in the thyme. Slowly drizzle in the remaining 2 cups vegetable broth, stirring constantly with a whisk. Stir in the Tamari, bay leaf and the pureed onion mixture. Cook, stirring frequently, until the mixture comes to a boil. Let boil, stirring constantly, until it has thickened slightly, about 3-4 more minutes.

Remove from heat and discard the bay leaf. Stir in the balsamic vinegar. Taste and add additional salt and pepper if desired before serving.