Combine the onions, garlic, and shallots in a roasting pan in a single layer. Add the olive oil and seasoning salt, and toss to coat. Roast until well browned, about 1 1/2 hours.
Remove the pan from the oven and set over 2 burners on medium-low heat. Add 2 cups of chicken stock, sage, thyme and salt. Cook for 10 minutes, scraping the bottom of the pan with a wooden spoon to incorporate any of the caramelized bits from the bottom.
Transfer the mixture to a blender and puree until smooth, about 2 minutes.
Transfer the mixture to a large pot over medium-low heat. Add remaining 4 cups chicken stock and balsamic vinegar, and stir to combine. Bring to a simmer and stir in cream. Serve with French bread.