In a food processor, combine almond flour, coconut flour, arrowroot powder, Italian seasoning, and salt. Pulse until thoroughly combined.
With the food processor running, add in apple cider vinegar. Once it has distributed evenly, add in the egg.
Add water teaspoon by teaspoon, as needed, until the dough forms into a ball. The dough should be firm, but sticky to touch and with no creases.
Wrap dough in plastic wrap and knead it through the plastic for a couple of minutes.
Place the dough in the refrigerator to rest for 30 minutes (or up to 5 days).
Cut dough into 4 pieces, roll out into logs, and slice off even-sized pieces. This will create evenly sized pasta. Lightly dust a cutting board and pasta pieces with coconut flour. Place a piece of pasta on your cutting board, and use a knife to press the dough upwards and towards you. This will curl the pasta into the shape you want.
Place shaped pasta in the freezer for 15 minutes.
In a skillet over low heat, add butter and oil. Once warm, add in chilled pasta and toss.
For al dente pasta, cook until it just begins to develop some color.
Toss pasta with your favorite sauce.