Make the dough: Fill a small bowl with ice water and set aside. To the work bowl of a food processor, add the flour, salt, and black pepper, and pulse to combine. Scatter over the butter and process until you have pea-size clumps, 10–15 pulses. Pour 2 tablespoons of the ice water through the feed tube and pulse 2–4 times to incorporate. Add additional ice water by the tablespoon as needed until the dough holds together when pinched, about 8 tablespoons total.
Turn the dough onto a clean work surface and form into a ball. Wrap in plastic, then press into a 1-inch-thick square. Refrigerate for 1 hour, or up to 2 days.
Make the topping: To the bowl of a food processor, add the ricotta, 2 tablespoons of the olive oil, ½ teaspoon of the salt, and lemon zest, and process until smooth. If the mixture looks dry, add up to 1 tablespoon more olive oil. Cover and refrigerate.
Cut off the carrot greens, wash them thoroughly under cold water to remove any grit, and set aside 2 tablespoons of the leaves for garnish (reserve the remaining greens for another use). Using a vegetable peeler, peel the carrots (discard the peels), then use the peeler to slice them into thick ribbons. If using various colors, separate by hue; set aside.
In a large bowl, whisk together the lemon juice, coriander, caraway, remaining oil, and remaining salt; set aside.
Position a rack in the top third of the oven and preheat to 400°F. On a floured surface, roll the dough into a 11-by-16-inch rectangle. Use a knife to square off the edges if desired. Transfer to a parchment-lined baking sheet and refrigerate until firm, about 10 minutes. Using a spoon or offset spatula, spread the ricotta mixture evenly over the crust, leaving a ½-inch border. Using a pastry brush, moisten the edges lightly with olive oil. Transfer to the oven and bake until the crust is lightly golden, 16–18 minutes.
Remove the tart from the oven. To the bowl with the dressing, add one quarter of the carrot ribbons and toss to coat, squeezing lightly to allow any excess liquid to drip back into the bowl. Pile the carrots atop one quadrant of the ricotta, and repeat with the remaining carrots. (For an ombré effect, overlap the colors slightly). Reserve any remaining dressing.
Return the tart to the oven and bake, rotating the pan halfway through cooking, until the crust is golden brown, 10–12 minutes more. Drizzle the carrots with the reserved dressing. Sprinkle with the cilantro, reserved carrot leaves, and flaky salt. Cut into slices and serve warm or at room temperature.