Preheat your oven to 425°F / 220°C.
Line a large baking sheet with parchment paper.
In a medium bowl, thoroughly combine the room temperature goat cheese and the finely diced vegetable mixture until evenly distributed.
Set aside.
Working with a small amount of kataifi at a time (keep the rest covered with a damp cloth), pull off a bundle of strands and gently spread it into a rectangle approximately 1 inch by 4 inches.
Brush the kataifi rectangle generously with melted butter. Scoop about a tablespoon of the cheese mixture and form it into a cylinder about 1 inch long.
Place the cheese log at one end of the kataifi and roll it up tightly.
Place the wrapped roll seam-side down on the prepared baking sheet.
Repeat with the remaining kataifi and cheese filling, arranging them in a single layer.
Bake for 15-20 minutes, or until the kataifi is a deep golden brown and wonderfully crisp.
Remove from the oven and let cool for a minute before serving warm.
Keep your kataifi dough covered with a damp kitchen towel while you work. It dries out incredibly fast, which makes it brittle and difficult to roll.