Preheat the oven to 400 degrees F and line a plate with paper towels.
Pull off the leaves from the base of the cauliflower and cut off the stem, but do not cut out the core. Slice the cauliflower into 1-inch thick slices, aiming for about 3 nice "steaks" from the center. The rest will break into smaller florets, and that is okay.
Mix the flour with 1 teaspoon salt in a shallow bowl or pie plate. Put the eggs in another shallow bowl and panko in a third shallow bowl.
Add 1/4 inch olive oil to a large skillet and heat over medium-high heat until shimmering.
Working with the larger pieces first, add the cauliflower to the flour and turn to coat. Shake off the excess, then dip in the egg to coat. Let the excess egg drip off, then coat thoroughly in the panko. Fry the cauliflower in batches to avoid overcrowding, turning once, until golden brown on both sides, 6 to 8 minutes total. Transfer to the lined plate to drain and sprinkle with salt. Repeat with the remaining smaller pieces of cauliflower (leave out any tiny crumbly pieces).
Spread 1 cup marinara sauce on the bottom of a 9-by-13-inch baking dish. Arrange the fried cauliflower on top, then spoon 1 cup of the sauce on top of the cauliflower. Arrange the mozzarella over the sauce, then spoon the remaining 1/2 cup marinara over the top. Sprinkle with the Parmesan and bake until bubbling and lightly browned in spots, about 35 minutes. Sprinkle with the basil and serve.
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