In a saucepan, heat the 4 cups of stock to a simmer.
Melt the butter in a medium saucepan over medium heat. Add the chopped onion, carrot and celery. Cook the mirepoix until the vegetables are softened and golden, 6-8 minutes.
Sprinkle in the flour and stir together with the mirepoix. Cook until the roux is dark golden brown, about 7-10 minutes, stirring often.
Add the stock. When the roux is ready, slowly pour in the warm stock while whisking vigorously and constantly to ensure the sauce is lump-free.
Add the tomato purée and herbs. Whisk in the tomato purée, bay leaf and fresh thyme. Bring to a boil.
Once boiling, reduce the heat to a simmer and simmer, uncovered, until the sauce reduces by a third, about 30-45 minutes. Stir occasionally. Season the sauce to taste with salt and pepper.
Strain the sauce. Strain the sauce through a cheesecloth or a fine mesh strainer. Discard the solids.
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