Preheat oven to 400°. Line a rimmed baking sheet with parchment paper.
In a small bowl, stir together sweet potato, olive oil, and salt. Spread sweet potato mixture in an even layer on prepared baking sheet.
Bake until lightly golden and tender, 7 to 10 minutes. Let cool completely on baking sheet.
In a small bowl, stir together goat cheese, cream cheese, carrot, parsley, and thyme until well combined. Stir in cooled sweet potato.
Spread cheese mixture in an even layer onto 4 bread slices. Top with remaining bread slices to make 4 whole sandwiches. Using a long, serrated bread knife in a gentle sawing motion, trim and discard crusts from sandwiches to make 4x2-inch rectangles. Cut each sandwich into 2 (2-inch) squares. Cut each square in half diagonally to create a total of 16 triangular sandwiches. Serve immediately, or cover with damp paper towels, place in a covered container, refrigerate, and serve within 2 hours.
Recipe by TeaTime Magazine at https://teatimemagazine.com/herbed-goat-cheese-carrot-sweet-potato-tea-sandwiches/