Yeah, you can. You can connect with BNB/Aaalanche bridge team for this, maybe they will deploy the pegged token for you, but at the same time you need to provide liquidity for them.
And you can also deploy your own contracts on Aaalanche/Ethereum, then use a third part bridge, such as cBridge, e.g. you can add liquidity on this pool by 1:1 for your original token and the pegged token, as for the price, just make sure the cross-chain always works, If the prices don't match, someone will arbitrage.