Preheat the oven to 350°F. Grease a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, 1/4 cup sugar, olive oil, and rosemary until well mixed. Press mixture onto the bottom of the prepared pan.
In a large bowl, beat cream cheese and 1 cup sugar until smooth. Add eggs, one at a time, beating well after each addition. Stir in vanilla extract and chopped butter pecans. Pour mixture onto the prepared crust.
Bake for 45-55 minutes or until the center is almost set. Remove from the oven and cool on a wire rack for 10 minutes.
In a small saucepan, melt the toffee bits over low heat until smooth, stirring frequently. Drizzle the toffee over the cheesecake. Let the cheesecake cool to room temperature, then chill for at least 2 hours before serving.