Prepare custard: In a medium bowl, whisk egg, cane juice, flour and vanilla until well combined. In a small saucepan, heat milk on medium until small bubbles form around edges of pan. Slowly add egg mixture, whisking constantly until combined. Cook, stirring constantly with a wooden spoon, until beginning to boil and thick enough to coat back of spoon, 1 to 2 minutes. Spoon custard into a separate medium bowl and let cool slightly. Cover surface with plastic wrap and refrigerate until chilled, about 30 minutes. Wipe out saucepan.
Meanwhile, preheat oven to 400°F. Arrange 1 sheet phyllo on a flat surface. (TIP: Cover remaining sheets with damp paper towel to prevent drying.) Lightly brush top of sheet with 1 tsp butter and sprinkle with one-third of cinnamon. Repeat with remaining sheets, butter and cinnamon. Stack sheets, butter side up, to form 3 layers. Cut stack in half lengthwise and stack the 2 halves to form 6 layers. Cut this stack in half lengthwise, then slice each stack crosswise into thirds to make 6 rectangles total.
Line a muffin tin with phyllo, pressing each rectangle down with your fingers to set into cups. Bake until golden brown and bottoms are crisp when lightly touched, 8 to 10 minutes. Remove from oven and set aside until cool enough to handle. Transfer pastry shells to a wire rack to cool completely.
Just prior to serving, spoon 1 1/2 tbsp custard into each pastry shell; set aside. Prepare caramel: In small saucepan, combine Sucanat and 3 tbsp water and heat on medium-high. Cook, stirring constantly, until Sucanat dissolves, about 1 minute. Bring to a boil, then reduce heat to medium-low and simmer, stirring occasionally, until thickened and reduced, about 2 minutes. (TIP: Caramel can burn easily, so watch carefully. To check if caramel is fully thickened, run a wooden spoon along the bottom of pan; if the spoon creates a clean line, the sauce is ready.)
Spoon caramel over top of tarts, dividing evenly. Set aside until caramel cools and hardens, 3 to 5 minutes. Serve immediately.