In a mixing bowl, combine the softened cream cheese, dill, lemon juice, garlic powder, onion powder, salt, and pepper. Mix until smooth and well combined.
Lay out the slices of whole grain bread on a clean surface. Spread a generous layer of the cream cheese mixture on each slice.
On half of the bread slices, layer the thin cucumber slices and grated carrots evenly. Top with another slice of bread, cream cheese side down, to form a sandwich.
Press down gently on each sandwich to help them hold together. If desired, trim the crusts off for a neater presentation.
Cut each sandwich into quarters or halves, depending on your preference. Arrange on a serving platter and garnish with fresh parsley if desired.