In food processor, pulse the graham crackers and pecans until fine crumbs. In a medium bowl, combine the prepared crumbs, sugar, cinnamon and melted butter and mix well. Press the mixture evenly onto the bottom and slightly up the sides of an ungreased 9-inch spring form pan. Refrigerate while preparing the filling.
Preheat the oven to 350° F (175° C).
In the large mixing bowl with paddle attachment, beat the cream cheese until fluffy on medium speed, about 2 minutes. (Or you can also use electric hand mixer.) Add condensed and beat for another minute. Stir in the carrot juice. Then add cinnamon, vanilla extract and salt and mix until well combined, about 1 minute. Beat in the eggs one at a time and mix just until combined on low speed. (Don’t beat the mixture too long and too fast after you add the eggs. Otherwise too much air will incorporate to the batter, which might cause a crack in the cooked cheesecake.) Transfer the batter into the prepared crust.
Bake for 50-60 minutes, or until the edges of the cheesecake is set, but the center is slightly wobbly. Cool on a wire rack for 5 minutes. Carefully run a knife around edge of the pan to loosen; cool for another hour. Then refrigerate for at least an hour to cool completely.
To make the frosting, beat the cream cheese and sour cream in a mixing bowl with whisk attachment, until well combined. Add powdered sugar and vanilla extract and continue to beat until smooth.
Once the cheesecake is completely cooled, remove springform sides of the pan. Spread the frosting evenly and decorate with pecan halves, if desired.