The cilantro here is fragrant even after cooking, and the vegetables' sweetness is offset by the toasted spices. Roasting beets provides more intense flavor but requires peeling them raw, which can leave hands red; consider wearing gloves.
Preheat oven to 425 degrees. Rub beets and carrots all over with oil. Season with salt. Spread in a single layer on a rimmed baking sheet; roast, turning once, until browned in spots and tender, 25 to 30 minutes for beets, 30 to 35 minutes for carrots. (Start checking at low end of range and remove any that are done.)
Lightly brush a 10-by-15-inch jelly-roll pan with oil. Brush 1 phyllo sheet with oil; fit into pan, leaving a 1-inch overhang. (Keep remaining phyllo covered with plastic as you work.) Top with a second sheet in a slightly different position; brush with oil. Repeat with remaining phyllo to make a crust with a 1-inch overhang all around. Fold edges under to double thickness. (Don't worry if some pieces crack along edge.)
Crumple 6 pieces of foil into a rectangle the size of interior of tart; fit into crust. Bake until edges are golden, 8 to 10 minutes. Remove foil. Bake until crustis golden all over, 6 to 7 minutes. Transfer to a wire rack; let cool. Reduce oven to 375 degrees.
Meanwhile, in a food processor, blend chermoula, sour cream, and eggs. Pour mixture into baked crust; top with carrots and beets. Bake until filling is set, about 15 minutes. Serve warm or room temperature, or store, tented with foil, at room temperature up to 1 day.