For the dressing: Combine the carrots, grapeseed oil, rice wine vinegar, soy sauce, sesame oil, sugar, garlic, ginger and red onion in a blender and blend until smooth. If the dressing is too thick, add 1 tablespoon water and blend until incorporated. Transfer to a bowl and set aside.
For the salad: Arrange the quartered romaine, cut-side up, on a serving platter. Spoon a generous amount of dressing over the top. Scatter the bacon over the lettuce, top with the tomatoes and grated carrot, and sprinkle with the chives.
Store any extra dressing in a sealed container in the refrigerator for up to one week.