Make the Polenta: Bring the chicken stock, butter, pepper, and salt to a boil in a heavy-bottomed pot. While whisking the hot stock in a quick circular motion, "rain" in the polenta by letting it stream through your fingers. (This will prevent lumping.)
Reduce the polenta to a gentle simmer; it must be stirred constantly for 25 to 35 minutes to prevent lumps or scorching. Be very careful when stirring, the mixture is very hot (think lava) and can burn you if it boils and sputters. If it begins to boil cover the pot and reduce the heat until boiling stops!
The polenta is cooked when it is no longer grainy and has become creamy. (My grandmother says good polenta takes 30 minutes, great polenta takes 1 hour).
Stir in the Parmesan and basil and pour onto a buttered sheet pan to cool. When cool, cover with plastic wrap and refrigerate. Cut the polenta into any shape you desire that's structurally sound. In other words, a shape that won't fall apart on the grill easily, or be difficult to remove from the sheet pan after roasting. Squares, triangles, stars etc.
Make the Marinade and Vegetables: Whisk together the vinegar and garlic. While whisking, drizzle in the oil to make a smooth dressing. Season with salt and pepper, to taste. Toss the vegetables with the marinade.
When ready to serve, preheat an outdoor grill or indoor grill pan.
Brush the polenta lightly on both sides with olive oil and grill, turning once, until the edges are brown and crispy.
At the same time grill the vegetables until they are tender but still firm.
Pile the vegetables on top of the polenta, then stand back and wait for the applause!