There was another comment that mentioned that there's an issue with port killing code on Windows: https://news.ycombinator.com/item?id=43614145
I just published a new version of the @browsermcp/mcp library (version 0.1.1) that handles the error better until I can investigate further so it should hopefully work now if you're using @browsermcp/mcp@latest.
FWIW, Claude Desktop currently has a bug where it tries to start the server twice, which is why the MCP server tries to kill the process from a previous invocation: https://github.com/modelcontextprotocol/servers/issues/812