Preheat the panini grill to high heat. Ensure the grill is on a slight tilt (not completely flat) and be sure to attach your drip tray.
Brush the cut side of the tomatoes with olive oil. Season with salt and pepper. Place the tomatoes, cut side down, onto the panini grill. Lower the top grate to just above the tomatoes without touching them. Grill tomatoes for 10-12 minutes until the outer skins are wrinkly and the tomatoes are soft. Check the tomatoes often, as some may cook faster than others. Remove the tomatoes from the grill and sprinkle with basil.
Brush melted butter onto the outer sides of each slice of bread. For each sandwich, layer two slices of bacon, two grilled tomatoes and 1/4 of the cheese in between two slices of bread (buttered side out). Grill the panini for 5-7 minutes until the cheese is melted and the bread is toasted. Serve immediately and enjoy!