How to Make It
Lightly grease a 13- by 9- by 2-inch baking pan or dish. Stir cornmeal and 1 cup cold water in a medium bowl until blended to a thick paste.
In a large saucepan, bring 2 3/4 cups water and the salt to a boil. Stir in the cornmeal paste and return to a boil, stirring frequently. Reduce the heat to low and cook, stirring occasionally, until the polenta thickens enough to hold the trail of a spoon, 8 to 10 minutes. (It should resemble soft mashed potatoes.)
Remove polenta from heat and add the butter, stirring until melted. Working quickly, pour the polenta into the prepared baking pan and spread it evenly with a spatula. Let it cool, then cover pan and refrigerate for at least 1 hour, or until the polenta is chilled through and firm.
Heat oven to 400º. Press small cookie cutters into the pan of chilled polenta to cut out shapes. Use spatula to transfer the shapes to a lightly oiled nonstick baking pan. With a pastry brush or a small, clean paintbrush, paint the top and sides of each shape with the olive oil. Bake for 15 to 20 minutes, or until the polenta shapes are lightly browned, crispy around the edges, and soft inside. Serve warm.
How Kids Can Help: Measure the ingredients; grease the baking dish; stir cornmeal and water; press out shapes and transfer to baking pan; brush olive oil on polenta shapes.