Bailey's Irish Cream Cheesecake

1 tablespoon unsalted butter, softened
2 cups graham cracker crumbs
2 cups granulated sugar, divided
1/2 cup unsalted butter, melted
2 1/4 pounds (36 ounces) cream cheese, softened
5 large eggs (at room temperature)
1 teaspoon pure vanilla extract
1 cup Bailey