Pre-heat oven to 400 degrees.
Combine fiddleheads with ½ Tbsp. olive oil and salt and pepper and place on one third of a parchment paper covered baking sheet.
Combine heirloom carrots with 1 Tbsp olive oil and salt and pepper and place next to fiddleheads on baking sheet.
Combine haricot vert with 1 Tbsp olive oil and salt and pepper and place next to carrots on baking sheet.
Roast vegetables at 400 degrees for about 20-25 minutes, until lightly browned.
Arrange vegetables on a platter and top with crumbled feta cheese and parsley.