Preheat oven to 190 C (375 F) and line a baking tray with baking paper.
In a mixing bowl, use fingers to rub butter and flour together until the mixture resembles fine breadcrumbs.
Add water one tablespoon at a time while mixing. Use hands to bring dough together.
Add cheese and carrot and squish into the dough until well combined.
Place dough on a lightly floured surface and roll flat with a rolling pin (dust rolling pin with flour to keep it from sticking).
Cut into sticks about 1 cm wide and 5 cm long.
Place sticks onto baking tray, evenly spaced.
Bake for 15 mins.