Melt 1 teaspoon butter and olive oil in a saucepan over medium-low heat. Cook and stir 2/3 of the corn, with a pinch of salt and a pinch of cayenne pepper in the hot butter and oil until the corn is fragrant and golden, about 10 minutes. Add garlic; cook and stir until fragrant, about 30 seconds.
Pour 2 cups water into corn mixture; bring to a simmer and whisk polenta into mixture. Bring to a simmer again, reduce heat to low, and simmer, stirring occasionally, until mixture is thick and polenta absorbs the water, 20 minutes. Add remaining 1/2 cup water and stir; cook for until water is completely absorbed, about 10 minutes more.
Stir remaining corn and 1 teaspoon butter into polenta mixture. Remove from heat, cover the pot, and let sit for 5 minutes before serving.