Preheat the oven to 325 degrees F.
For the crust: Butter the bottom of a 9-inch spring form pan with some of the melted butter. In a small bowl, toss remaining butter with the graham cracker crumbs. Sprinkle the bottom of the pan with the crumbs. Wrap the outside and bottom of the pan in a large piece of foil. (This is to prevent water from seeping through during the baking.)
For the Candied Jalapenos: In a small saucepan, combine jalapenos, sugar, and water. Simmer until jalapenos are softened, about 20 minutes. Drain, reserving the jalapenos and syrup separately. Cover the crust with the drained jalapenos. Set aside.
For the Cheesecake Batter: In the bowl of an electric mixer fitted with the paddle attachment, beat the cheese with the sugar until light and smooth. Add the eggs 1 at a time, scraping down the bowl between additions. Add remaining ingredients, including the reserved syrup, and mix until combined. Pour batter over jalapenos.
Place pan inside a roasting pan. Add hot water to come halfway up the sides of the spring form pan. Bake until cheesecake is just set, but still a little wobbly in the center, about 1 hour. Cool and refrigerate until completely set, at least several hours, up to overnight.