Step 1 Bring 2 cups water to a boil in a medium saucepan over high heat, then add salt and whisk in polenta in a steady stream. Lower heat to a simmer and cook for 10 minutes, stirring occasionally with a whisk to avoid lumps and until the polenta is thickened. Add the olive oil and Parmigiano-Reggiano and whisk to incorporate. Remove the pan from heat.
Step 2 Pour the polenta onto a parchment-lined baking sheet with sides. Using a spatula, smooth the polenta to an even height of one-half inch. Refrigerate, uncovered, until set, about 45 minutes. Remove the chilled polenta from the pan and cut into one-half-inch cubes.
Step 3Fill a large saute pan with enough canola oil to cover the bottom by 1 1/2 inches. Heat the oil over high heat until a thermometer inserted reads 375 degrees. Adjust the heat to maintain this temperature. Fry a few croutons at a time, leaving enough space so they do not stick together. Be careful that the croutons do not stick to the bottom of the pan and burn. Fry the croutons until golden, about 2 minutes, then remove and set them on paper towels to drain.