Make the latkes: Using the shredding attachment on a food processor (or mandoline), shred the potatoes, onions and garlic.
Line a colander with 2 layers of cheesecloth and set it over a bowl or in the sink. Add the shredded vegetables to the cheesecloth and sprinkle with 2 teaspoons kosher salt. Let drain 30 to 45 minutes. Gather up the edges of the cheesecloth and use your hands to squeeze out any excess moisture.
In a large bowl, mix together the eggs, lemon juice, a few grinds of pepper and the panko. Mix in the potato mixture; stir in more panko, 1 tablespoon at a time, if the mixture seems too wet. Stir in the scallions.
In a large cast-iron skillet, heat 1/4 inch of vegetable oil over medium-high heat until shimmering (it’s ready when a strand of potato added to the oil immediately starts to sizzle). Using an ice cream scoop, add blobs of the mixture to the hot oil, spacing them out so as not to crowd the pan. Press down lightly with a spatula to make 1/2-inch-thick patties. Fry until golden brown, a few minutes per side.
Transfer the latkes to a rack or paper towel–lined baking sheet; sprinkle with kosher salt or flaky salt. Repeat with the remaining mixture, adding more oil to the pan as needed.
For the pizza latkes: Preheat the oven to 450 degrees F and line 2 baking sheets with parchment paper. Arrange the latkes on the baking sheets, then top each one with about 2 teaspoons marinara sauce and 1 slice cheese. Bake until the cheese is melted, about 7 minutes. Top with the grated Parmesan, red pepper flakes and basil.
