  For each $n\ge 3$, we construct an $O(2)\times O(n-1)$-invariant ancient Ricci flow on the $n$-sphere $S^n$ with positive curvature operator and bounded "girth". As time approaches minus infinity, it decomposes into a flat cylinder $S^1\times \mathbb{R}^{n-1}$ in the "waist" region and an $(n-2)$-plane of cigar solitons around any point in the "tip" region (both of which are of the same scale). This solution appears to be new, even in dimension three. 
Ancient Ricci pancakes of bounded girth