Heat oil and garlic in a large (12-inch) skillet over medium-high heat until garlic just starts to sizzle. Immediately add spinach and stir, scraping garlic into spinach, until spinach just wilts, a few minutes. Lightly salt and pepper the spinach and turn it onto a cutting board; coarsely chop.
Using a potato masher or a large fork, mash potatoes. (Small lumps are good.) Place potatoes, spinach, flour and yeast in a large bowl. Mix to combine. Taste and adjust seasoning, including salt and pepper to taste. Divide mixture into 8 portions and form into patties; dredge in panko.
Meanwhile, heat 3 tablespoons of oil in each of 2 medium (10-inch) skillets over medium-high heat. Add patties and cook, turning only once (and reducing heat to medium if cakes start browning too quickly), until golden brown on both side, 8 to 10 minutes total. Remove from pan and serve immediately.