Preheat oven to 400 degrees.
Combine the first four ingredients and stir to combine.
Using your hands, add the carrots to the flour mixture coating the carrot pieces with flour.
Add the oil and work with your hands to bring the dough together.
(You really have to be patient with working this dough together so that the flour absorbs the oil. If you are concerned that it is not coming together, just add 1 extra teaspoon of oil to the dough and work it with your hands forming a ball until it comes together.)
Form the carrot parmesan dough into a flat rectangular disk and allow to rest for 1-2 minutes then roll out 1/2 inch thick on parchment paper or a dry clean surface.
Using a sharp knife, cut the dough into sticks, 2 inches long by 1/4 inch wide.
Bake on a Silpat or parchment lined cookie sheet for 15-17 minutes.
To Freeze: After step 6, place onto a baking sheet and freeze for 30 minutes. Remove and place in a ziploc bag, label and freeze. When ready, follow steps 7, adding an additional 2-3 minutes baking time.