Lightly coat a 13 x 9 x 2-inch baking dish with nonstick cooking spray. In a large saucepan, combine milk, 1 cup water, garlic powder, salt and pepper. Bring to a simmer over medium-high heat. Gradually whisk in polenta. Cook, whisking continuously, for about 2 minutes, until thick. Add a little hot water if mixture becomes too thick. Stir in Asiago cheese and fresh basil. Spread polenta in prepared baking dish and allow to set at room temperature.
Heat olive oil in a large nonstick skillet over medium to medium-high heat. Add onions and cook 8 minutes, stirring occasionally, until golden. Remove to a plate and wipe out skillet.
Heat olive oil in same skillet over medium heat. Add chard (in batches) and garlic and cook 5 minutes, stirring occasionally. Season with Italian seasoning, salt and pepper. Stir in beans and heat through.
Assemble casserole. Heat oven to 350°. Spoon chard and beans evenly over polenta. Sprinkle 1/2 cup of the Asiago cheese over chard and beans. Scatter onions and remaining cheese over top. Bake, uncovered, at 350° for 15 minutes.
Allow to cool slightly before slicing. May also be served at room temperature.