Preheat the oven to 350 degrees F (175 degrees C).

Combine graham cracker crumbs, pecans, sugar, and rosemary in a bowl; stir in butter. Press crust into the bottom of a 9-inch springform pan and set aside.

Combine Neufchatel cheese and sugar in a mixing bowl. Beat using an electric mixer until smooth. Add eggs and beat until combined. Add flour, lime juice, lime zest, and rosemary; beat until blended. Pour filling into the prepared crust.

Bake in the preheated oven until almost set, about 55 minutes. Remove from the oven and let cool for 5 minutes, leaving oven on.

Combine sour cream, sugar, and lime zest for topping in a bowl. Spread over cheesecake.

Return cheesecake to the hot oven and bake for 5 minutes.

Remove from the oven and let cool on a wire rack for 10 minutes. Run a knife carefully around the sides of the pan to loosen; let cool for at least 1 hour. Refrigerate for 8 hours to overnight. Remove sides of the pan. Let sit for 30 minutes before serving.