Begin by pre-heating oven to 375 degrees Fahrenheit.
Wash the beets well and slice beets very thinly using a mandolin and set aside on a plate.
(*Tip: Slice the yellow before before the red one so you don't risk staining the lighter beets.)
Unroll phyllo sheets and place 2 phyllo on a baking sheet. Brush all over with olive oil and then place two more sheets on top and brush with olive oil. Finally layer the last two phyllo on top and fold in the edges, making a border. Brush with olive oil so edges seal.
Arrange beet slices on top of phyllo and brush everything with the rest of the olive oil.
Scatter crumbled feta on top and some of the fresh thyme leaves and a good sprinkle of sea salt.
Bake for 30 minutes, until the phyllo is lightly golden brown.