In a large baking sheet place eggplant & Havarti cheese and rub with ½ cup of olive oil and season with salt.
Grill eggplant over hot grill, griddle, or cast-iron skillet. Allow to mark well and put back onto the baking sheet to cool.
Grill Havarti quickly to brown and place one piece on each slice of eggplant and roll.
Stir together all ingredients for chimichurri into a bowl except salt and lemon.
Spoon chimichurri over each eggplant roll and allow to marinate at room temperature. Reserve some chimichurri for plating.
When ready to serve, place onto a plate dressed with remaining chimichurri, a squeeze of lemon, and a sprinkle of sea salt.