docs: Update quickstart instructions for testing with inspector

Change from 'uv run mcp dev' to the simpler two-step approach:
1. Run server with 'uv run --with mcp server.py'
2. Open inspector with 'npx -y @modelcontextprotocol/inspector' and connect manually

This avoids the complexity of mcp dev trying to manage stdio vs HTTP transport
and gives users more control over the connection.

Author: domdomegg

README.md

@@ -177,18 +177,26 @@ if __name__ == "__main__":
 _Full example: [examples/snippets/servers/fastmcp_quickstart.py](https://github.com/modelcontextprotocol/python-sdk/blob/main/examples/snippets/servers/fastmcp_quickstart.py)_
 <!-- /snippet-source -->
 
-You can install this server in [Claude Code](https://docs.claude.com/en/docs/claude-code/mcp) and interact with it right away by running:
+You can install this server in [Claude Code](https://docs.claude.com/en/docs/claude-code/mcp) and interact with it right away. First, run the server:
+
+```bash
+uv run --with mcp examples/snippets/servers/fastmcp_quickstart.py
+```
+
+Then add it to Claude Code:
 
 ```bash
 claude mcp add --transport http my-server http://localhost:8000/mcp
 ```
 
-Alternatively, you can test it with the MCP Inspector:
+Alternatively, you can test it with the MCP Inspector. Start the server as above, then in a separate terminal:
 
 ```bash
-uv run mcp dev server.py
+npx -y @modelcontextprotocol/inspector
 ```
 
+In the inspector UI, connect to `http://localhost:8000/mcp`.
+
 ## What is MCP?
 
 The [Model Context Protocol (MCP)](https://modelcontextprotocol.io) lets you build servers that expose data and functionality to LLM applications in a secure, standardized way. Think of it like a web API, but specifically designed for LLM interactions. MCP servers can:

docs/index.md

@@ -42,10 +42,16 @@ if __name__ == "__main__":
     mcp.run(transport="streamable-http")
 ```
 
-Test it with the [MCP Inspector](https://github.com/modelcontextprotocol/inspector):
+Run the server:
 
 ```bash
-uv run mcp dev server.py
+uv run --with mcp server.py
+```
+
+Then open the [MCP Inspector](https://github.com/modelcontextprotocol/inspector) and connect to `http://localhost:8000/mcp`:
+
+```bash
+npx -y @modelcontextprotocol/inspector
 ```
 
 ## Getting Started