Preheat the oven to 400 degrees F. Peel the carrots and discard the skins. Using a vegetable peeler, peel long, wide ribbons of carrot until you can no longer make ribbons. Combine the carrot ribbons with the sugar and 1 1/2 cups water in a large saucepan. Bring to a simmer over high heat, stirring occasionally, then immediately remove the carrots with tongs to a rimmed baking sheet. Spread into a single layer and let cool, pouring any syrup from the bottom of the baking sheet back into the pot. Simmer the syrup until lots of small bubbles form on the surface and it is a bright orange color, about 10 minutes. (You should have 1 cup of syrup left.) Let cool for 5 minutes, then stir in the lemon juice. Remove to a heatproof container and refrigerate until cool, 1 hour.
Meanwhile, combine the apricots and raisins in a food processor and pulse until roughly chopped, about 10 pulses. Add the nuts and 1/4 teaspoon salt, scrape down the sides and pulse until the nuts are roughly chopped, another 10 pulses. Set aside.
Brush an 8-inch springform pan with butter and line with 1 sheet phyllo. Tuck any phyllo the hangs over the edge into the edges of the pan. Brush generously with butter and lay the next sheet of phyllo on top going in the other direction. Brush generously with butter and repeat this pattern with the remaining phyllo. Put the nut and fruit mixture into the pan and pack it down firmly so it is evenly spread out.
Arrange the carrot strips on a work surface next to each other so they are about 1-inch wide. Starting from one end, roll them up loosely. Put them on top of the nuts so you can see the spiral of the carrot. Repeat with the remaining carrots until the top is covered in 30 to 40 carrot flowers.
Put the pan on a baking sheet and bake until the phyllo is golden, 25 to 30 minutes. While it is still hot, drizzle the cold syrup all over the carrots until the nuts are just covered in syrup. Remove the sides of the pan and let cool until fully cooled and set, about 2 hours, before serving.
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