Brush an 8-by-8-by 2 1/2-inch glass baking dish with the oil. Bring the water and kosher salt to a boil in a heavy, medium saucepan over medium heat. Add the polenta using a whisk to incorporate. Reduce the heat. Let simmer for about 10 minutes, stirring frequently. Add the cream, using a whisk to incorporate. Cook until the consistency is soft and thick, about 10 minutes. Remove from the heat and add the Parmesan cheese, using a whisk to incorporate. Pour the polenta into the prepared baking dish and spread evenly into the dish using a large spatula or the back of a large spoon. Refrigerate until chilled.
To make the salsa: Mix the sun-dried tomatoes, basil, balsamic vinegar, garlic, and pepper together in a small bowl.
To assemble: Preheat the oven to 300 degrees F. Trim the edges of the polenta and cut into 36 squares. Top each square with 1/2 teaspoon of the salsa. Place on a foil- or parchment paper-lined baking sheet. Bake until slightly warm, 8 to 10 minutes. Serve warm.
The polenta and the salsa can be prepared up to 2 days in advance. The squares can be assembled up to 1 day in advance. Bake as directed.
Recipe from Cocktail Food, by Mary Corpening Barber and Sara Corpening Whiteford, published by Chronicle Books.