In a small saucepan, stir together 1 cup sugar, water, honey, and ½ cup brown sugar. Bring to a boil over medium heat. Once boiling, reduce heat to low and simmer, stirring occasionally, until sugar has dissolved, 2 to 3 minutes. Set aside to cool while preparing baklava.

In a food processor, pulse pistachios and pecans until finely chopped, about 12 pulses. Transfer nuts to a large bowl and add carrots, coconut, cinnamon, salt, ginger, cardamom, remaining ¼ cup sugar, and remaining 2 tablespoons brown sugar and stir to combine.

Adjust oven rack to lower-middle position and preheat oven to 350°F (175°C). With a pastry brush, brush bottom and sides of a 9- x 13-inch baking pan with melted ghee or butter.

Working with half of phyllo at a time, unroll phyllo onto a clean work surface and use a sharp knife to trim in to 9- x 13-inch rectangle to fit the prepared baking pan. Discard or reserve phyllo trimmings for another use. Repeat with remaining phyllo and stack phyllo together and cover with a damp paper towel. Place 1 phyllo sheet in baking pan, and brush top with ghee or butter. Top with another phyllo sheet and brush with ghee or butter. Continue layering 8 more phyllo sheets, brushing each layer with ghee or butter (a total of 10 sheets on bottom layer).

Sprinkle 1 cup of carrot mixture evenly over top sheet of phyllo. Place another phyllo sheet over carrot mixture, and brush with ghee. Continue layering 7 more phyllo sheets, brushing each layer with ghee or butter (a total of 8 phyllo sheets).

Sprinkle 2 cups of the remaining carrot mixture evenly over top sheet of phyllo. Place another phyllo sheet over carrot mixture, and brush with ghee. Continue layering 7 more phyllo sheets with butter (a total of 8 phyllo sheets). Sprinkle remaining carrot mixture over top phyllo sheet. Place another phyllo sheet over carrot mixture and brush with ghee or butter. Continue with remaining phyllo sheets until all phyllo sheets are used, ending with a final brushing of ghee.

Using a sharp knife, cut baklava lengthwise into 2-inch wide strips, making sure to cut all the way through the bottom of pastry. Cut baklava diagonally into 2-inch wide strips to create diamond shaped pieces.

Bake baklava until deep golden brown and crispy, rotating pan halfway through baking, about 1 hour. Remove from oven and immediately pour cooled honey syrup evenly over hot baklava, making sure to reach edges of pan. Set pan on a wire rack and cool, uncovered at room temperature, at least 2 hours or up to 24 hours before serving or storing.