Lay the slices of bread out on a clean work surface and brush 1 side of each with the olive oil. Turn the slices over and spread 1 tablespoon of Tomate Frito onto 4 of the slices, followed by layers of Manchego cheese and the Escalivada. Top with the corresponding slices of bread, olive oil-brushed sides facing up.
Heat a large sauté pan or griddle to medium-high. Add the sandwiches and cook on one side until golden brown and the cheese is slightly melted, about 2 minutes. Carefully flip the sandwiches over and cook until the other side is golden brown and the cheese is fully melted, about 3 minutes.
Alternatively, place the layered sandwich in a Panini-press and cook until golden brown and the cheese is melted. Remove the sandwiches from the heat and slice in half to serve.