Cut the butter into 3 equal parts. Spread 1 part of the butter all over both sides of both pieces of bread. Evenly sprinkle garlic powder and Italian seasoning on both sides of the bread. Melt 2nd part of the butter in a large and heavy nonstick skillet over medium heat. Once the butter is melted, add both slices of seasoned bread and cook, swirling around the pan occasionally, for about 2 minutes (bottom should be very lightly golden brown).
Transfer the bread slices onto a plate with the toasted side facing towards you. Add 3 cheese slices to each piece of bread (the cheese slices should barely overlap) and then add freshly sliced tomatoes, a sprinkle of salt + pepper, and pesto on one slice of bread. Sandwich the two pieces of bread and fillings together.
Melt the 3rd piece of butter and reduce the heat to medium-low. Add the sandwich and cook, swirling around the pan occasionally until the sandwich is an even golden brown and the cheese is all melty (4-5 minutes).
Remove from heat and lift the top piece of bread enough to add fresh basil to the sandwich and if desired, a small drizzle of balsamic reduction (see notes).
Serve the grilled cheese immediately with a side of the warmed soup.
Video
Notes
*You can buy balsamic reduction or make it very easily by combining 1 cup balsamic vinegar and 1/4 cup honey in a small saucepan. Place over high heat, bring to a boil, and then reduce the heat to low and simmer until the vinegar mixture has reduced to 1/3 cup (about 10 minutes). Set this balsamic reduction aside to cool before adding it to the sandwich.