Adjust one oven rack to lower middle position and second oven rack to highest position; heat oven to 400 degrees.

Toss together cheese, garlic, and thyme in a small bowl. Set aside.

Heat butter in a medium saucepan over medium heat until foaming; whisk in flour and cook until golden and bubbly, about 30 seconds.

Whisking constantly, gradually add chicken stock. Increase heat to high, add bay leaf, and bring to a boil.

Reduce heat to medium and simmer, stirring occasionally, until mixture thickens, about 2 minutes.

Remove from heat, remove and discard bay leaf; cover to keep sauce warm.

Alternating Yukon Gold and russet slices, arrange a third of potatoes in overlapping rows. Sprinkle potato layer evenly with 1/4 tsp of salt, 1/4 tsp pepper, and a third of cheese mixture.

Make a second layer with the same amount of potatoes, salt, pepper, and cheese.

Make a third layer with the same amount of potatoes, salt, and pepper, but reserve remaining cheese.

Pour warm sauce over potatoes, tilting pan side to side to distribute evenly.

Cover with foil and bake on lower-middle rack for 45 minutes. Remove foil and continue to bake until potatoes are tender, about 45 minutes longer.

Remove potatoes from oven and sprinkle with remaining cheese; bake on high rack until cheese is golden brown, about 5 minutes.

Cool 10 minutes and serve.