Preheat oven to 350° F. Grease an 11x7 inch baking dish with butter.
In a medium saucepan, bring 4 cups of water to a boil, add salt, and slowly whisk in the polenta. Lower the heat and simmer, uncovered, stirring often for 20 minutes.
Stir in the heavy cream and let cook, stirring constantly, until grits are tender and thick, about 5 minutes. Remove from the heat, add the butter, 3/4 cup of the cheese, and pepper.
While the polenta cooks: Heat 1 teaspoon of olive oil over medium heat. Add the bacon and cook until crisp. Remove from the pan and place onto paper towel lined plate, let cool then crumble. Add the onion and jalapenos to the skillet and let cook until the vegetables have begun to soften, about 5 minutes.
Add the jalapeno mixture to the polenta. Slowly stir in the lightly beaten eggs, then pour into the baking dish. Smooth the mixture out with a spatula, top with the remaining cheese and place into oven. Bake uncovered until the the polenta has set, about 35-40 minutes. Remove from the oven and let cool for a few minutes before serving.