Brown the onions in the hot oil. Add the rest of the vegetables and continue to brown. Add the tomato paste and cook until it begins to brown and caramelize.
Add the stock, and bring to a simmer. Whip the roux into the stock, making sure all lumps are dissolved. Return to a simmer and add the sachet.
Simmer for about 1 hour, and skim the surface if necessary. Strain the sauce through cheesecloth.