Combine the seasoning mix ingredients in a small bowl.
Melt 2 tablespoons of the butter with the olive oil in a 14-inch skillet or 5 quart pot, preferably nonstick, over high heat. As soon as the butter begins to sizzle, add all the vegetables, seasoning mix, and garlic. Stir well, then cover and cook, uncovered to stir and scrape the bottom of the pan frequently, for 4 minutes. You will see that the vegetables color is a little brighter and their texture is somewhat more tender, and the fragrance is crisp and earthy. Continue to cook, still uncovering to stir and scrape, until the vegetables begin to brown, about 4 minutes longer. Now the fennel will be wilted, transparent and tender, and the bottom of the pan will be dry. At this point the vegetables are partially cooked, but still retain some of their crunch. Add the tomato sauce, stir, re-cover and cook, uncovering every 2 or 3 minutes to stir, scrape and check to be sure the mixture is not going to scorch. Do this just until the vegetables are pasty and thickly coated with sauce, and the liquid has evaporated, about 7 to 8 minutes. If you feel that there might be a risk of over-browning, then lower the heat slightly. Add the stock, brown sugar, and the remaining 2 tablespoons butter. Stir very well and cook just until the butter is thoroughly melted into the sauce and the vegetables are tender, except for the celery which should still have a little crunch, about 2 to 3 minutes. Serve over hot pasta.
Recipe courtesy of Paul Prudhomme "Chef Paul Prudhomme's Louisiana Tastes"