Peel and finely chop the carrots and beets.
Put the chopped carrots and beets in a blender and blend until smooth.
In a small bowl, combine the râpé (grated carrots and beets), olive oil, lemon juice, salt, and pepper.
Lightly toast the whole grain bread.
Spread the râpé mixture on one slice of bread.
Add cheese or nuts if desired.
Top with another slice of bread to make a sandwich.