Place chopped tomatoes, cucumbers, peaches, scallions, garlic, Kosher salt, ¼ cup EVOO, mint leaves, basil leaves, and wine wine vinegar in a blender, then secure the lid. Blend until very smooth.
Though the gazpacho can be served immediately, it is meant to be served chilled. Transfer to a large bowl or tupperware, then seal and refrigerate. Taste and adjust seasoning as needed, stirring to mix in any additional Kosher salt and black pepper.
Divide between bowls, then garnish with additional black pepper and mint.