To start, slice your heirloom tomatoes into slices that are about 1/4" - 1/3" inch thick. Lay out paper towels on a baking sheet, then place the slices onto the pan. Take a pinch of salt and sprinkle over the tomato slices. Flip, then salt the other side. Leave the salted tomatoes on the paper towel-lined for at least 5 minutes, preferably 10. After the time has passed, use fresh, dry paper towels to pat off the excess water on the tomatoes. When done, set aside.
While tomatoes are being salted, make the basil aioli. Into a blender or food processor, add in all the ingredients. Grate the garlic into the mixture using a microplane or small grater. Blend aioli on high until basil leaves are minced into the aioli.
Toast all four pieces of your bread until golden brown.
Layer on some basil aioli on each piece of bread. Then, on two slices, layer on the salted tomatoes, bacon slices, and about 1 cup of arugula per sandwich. On top of the arugula, drizzle about 1 tsp olive oil and a pinch of salt. Then, top the sandwich with the last slices of bread.
Cut your sandwiches how you like, either straight in half or diagonally.
Enjoy!