Using a mandolin or a sharp knife, thinly slice the potatoes lengthwise.
3. Step
In a 13-inch (33-cm) cast iron skillet, layer slices of potatoes around the outside of the pan. Add another layer of potatoes, keeping them centered in the pan and moving clockwise until the pan is covered.
4. Step
Top with a third of the cheddar cheese, a third of the Gruyère cheese, and half of the ham.
5. Step
Add another layer of potato slices around the outside of the pan, then a add layer of slices around the center of the pan. Top with another third of the cheddar and Gruyère and the remaining ham slices.
6. Step
Add a final layer of potato slices around the center of the pan
7. Step
Top with the remaining cheddar and Gruyère cheese.
8. Step
Cover with greased aluminum foil and bake for 40 minutes.
9. Step
Remove the pan from the oven and increase the oven temperature to 400˚F (200˚C).
10. Step
In a medium bowl, combine the flour, garlic, Parmesan, salt, pepper and mix well.
11. Step
Slowly add in the cream, whisking until fully incorporated.
12. Step
Uncover the skillet and pour the cream mixture over potatoes, spreading evenly.
13. Step
Bake for another 10-15 minutes uncovered, until the cheese is melted and golden brown.
14. Step
Cool for at least 30 minutes, then slice and serve.
