Step #1. 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 it to an airtight container and store in the refrigerator until ready to serve.
Step #2. Add the spinach and arugula to a large bowl and toss to combine. Transfer to a serving platter and top with ripe peach slices, fresh blackberries, walnuts, and goat cheese.