You can buy them on Uniswap. Transfer your ETH to a metamask wallet and connect the extension to initiate the transfer.

Or you could just buy it on a centralized exchange. Plenty of exchanges offer it. Binance, coinbase, huobi, kraken, FTX and gemini are some examples.

you can trade BAT on kucoin without KYC, as long as you stay under 5BTC withdrawals per month or something

Brave Swap is in the Crypto Wallet brave://wallet

Can swap ETH for ETH or any ERC20