Add the olive oil, vinegar, Dijon mustard, honey, blackberries, and basil to a food processor container. Season with salt and black pepper, to taste, and process on high until thoroughly emulsified. Taste and add additional honey, salt, and/or black pepper, if desired. Transfer to an airtight container and store in the refrigerator until ready to serve.
Add the spinach and arugula to a large bowl and toss to combine. Transfer to a serving platter and top with sliced peaches, fresh blackberries, walnuts, and goat cheese.
Garnish with sprigs of fresh basil and drizzle some of the blackberry-basil vinaigrette on top. Serve immediately with remaining vinaigrette on the side. Enjoy