Combine oil, vinegar, pimento, parsley, green onions, garlic, sugar, basil, salt, and pepper in a jar with a tight-fitting lid
Seal the jar and shake vigorously to blend
Cut Cheddar block in half lengthwise, then cut crosswise into ¼-inch slices to form squares
Repeat with cream cheese
Arrange cheese squares alternately in a shallow baking dish with slices standing on edge
Pour marinade from the jar over top, cover, and refrigerate for at least 6 hours, or overnight
Transfer slices to a serving platter in an alternating pattern and spoon extra marinade over top
