Cook's Note: Preheat oven to 350 degrees F. Arrange the pine nuts in a single layer on a baking sheet. Bake until lightly toasted, 6-8 minutes. Cool completely before using.
For the polenta: Preheat the broiler. Bring 3 cups water and the salt to a boil in a medium saucepan over medium-high heat. Stir in the polenta and continue to stir until the polenta is thick, 5 to 8 minutes. Transfer the polenta to a sheet of parchment paper. Roll the polenta into a 2 1/2-diameter log. Refrigerate until cool, 30 minutes.
Spray a heavy baking sheet with vegetable oil cooking spray. Slice the polenta into 1/8-inch-thick slices. Cut each slice of polenta in half to make half-moon shapes and arrange in a single layer on the prepared baking sheet. Brush with the olive oil and sprinkle with the Parmesan. Broil until the cheese is golden, 6 to 7 minutes. Set aside to cool for 10 minutes.
For the goat cheese: Beat the goat cheese, cream, basil, salt and pepper in a medium bowl using an electric hand mixer on medium speed until light and fluffy, 1 minute. Stir in the pine nuts.
Using two spoons to measure, place 1/2 to 3/4 teaspoon-size dollops of the goat cheese mixture on top of the polenta slices and serve.