For the quails, wash the meat and pat dry with kitchen roll, salt and pepper inside and out and set aside.
Heat the olive oil in a suitable saucepan, sauté the very finely chopped onion until translucent, add the cleaned, coarsely chopped mushrooms and allow to color briefly.
Heat the chicken soup, add to the mushroom mixture, bring to a gentle simmer and pour in the polenta semolina in a thin stream, stirring constantly. Stir everything well, adding melted butter and vegetable oil occasionally, until the polenta has absorbed all the liquid. Now remove the saucepan from the heat, cover and leave to swell for 7 minutes.
In the meantime, preheat the oven to 220 °C. Fill the quails with the polenta-mushroom mixture, sew the opening tightly with kitchen twine. Keep the polenta warm.
Place quails, breast side up, in a roasting pan that has been well coated with vegetable oil and is about the same size and height as the roast. Drizzle the breast skin with a few drops of oil and top each with a sprig of thyme. After about 5 minutes, reduce the heat to 180 °C and roast for another 15 to 20 minutes, depending on the size of the quail. Meanwhile, brush the skin several times with the roasting residue.
As soon as the quails are cooked through and no more red juice comes out when the thighs are pierced, leave the quails to rest in the half-open oven for a few more minutes.