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Brush the outside of each slice of bread with olive oil.
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To build your sandwich, top one piece of bread with the Parmesan, followed by the tomatoes, basil and Havarti.
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Heat a grill pan over medium heat and lightly brush with olive oil to prevent sticking.
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Place the sandwich in the middle of the pan and grill it for 3-4 minutes. You want to cook this low and slow. Too high of a heat will result in a sandwich that isn't warm on the inside.
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When the sandwich is golden brown on one side, carefully flip it and cook on the other until it's golden brown and the cheese is melted.