siamese cosmos?

You have described fasciation. This is most often seen in flowering stems. Fasciated stems tend to be flattened and wider than normal, and flowers are as you describe, or there is a proliferation of buds, many times the normal number. This is an errant mutation that can occur in any plant and is not likely to recur. I saw a flower like this on a black-eyed Susan last year; the flower was normal in one dimension but the "black eye" was three times the width of normal, with correspondingly more petals.