Make the dressing: Whisk the vegetable oil and olive oil in a small bowl. In a large bowl, whisk the honey, vinegar, lemon juice, lemon zest, mustard, garlic, 1/2 teaspoon salt and a pinch of pepper.
Slowly whisk the oil mixture into the vinegar mixture until combined. Refrigerate at least 1 hour; store in an airtight container up to 1 week.
Make the salad: Toss the Brussels sprout leaves, dried blueberries and cranberries, almonds and 1/4 cup dressing in a large bowl. Pile the salad onto a plate. Top with the manchego and season with pepper. Serve with bagel chips, if desired.