Preheat oven to 325 F, or 425 F if oven-roasting vegetables.
Heat oil in oven proof pan until shimmering and add vegetables, stirring to coat. Either cook on stovetop, stirring every 5-10 minutes, until deep brown all over, or roast in oven. If oven-roasting, reduce temperature to 325 F.
Add tomato paste, if using, and stir to coat vegetables. Return to heat, stirring every 5-10 minutes, until paste is brick red. Add wine, if using, and deglaze pan. Reduce by half.
Add stock, deglazing pan if you did not do so with the wine. Add garlic, peppercorns, thyme, and bay, and bring to a simmer. Add tongues, and cover pan tightly. Transfer to oven and braise, checking after 1 1/2 hours for smaller tongues, and 3 hours for beef tongues.
Tongues are done when a paring knife slips easily to the thickest part of the tongue, and the thick membrane on the tongue peels easily.
When done, remove tongues from the braise 1-2 at a time and peel as soon as you can handle them. Return them to the braise and cool.