Arrange racks in middle and upper third of oven; preheat to 450 degrees F. Line a large rimmed baking sheet with foil.
Remove any outer leaves from cauliflower, but keep stems intact. Place on a cutting board, stem-side down. Using a large chef's knife, cut two 1-inch-thick slices from the center of each head to make 4 cauliflower "steaks." (Reserve remaining cauliflower for another use.) Place the steaks on the prepared baking sheet. Brush both sides with 1 tablespoon oil and sprinkle with salt.
Roast, turning halfway through, until the cauliflower steaks are tender, 30 to 35 minutes.
Meanwhile, heat the remaining 1 tablespoon oil in a large nonstick pan over medium-high heat. Add shallot and cook, stirring often, until softened, about 1 minute. Add spinach in batches and cook, stirring, until wilted, 3 to 5 minutes. Stir in dill, parsley, garlic and pepper. Cook, stirring, for 1 minute. Transfer the spinach mixture to a large mixing bowl. Stir in ricotta and feta.
Turn the broiler to high. Top each cauliflower steak with 1/2 cup of the spinach mixture and 2 tablespoons Cheddar. Broil the cauliflower until the cheese melts and starts to lightly brown, about 2 minutes. Serve immediately.
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