1. Bring milk to a simmer in a pan over medium-high heat. When bubbles form around edges, remove from heat and add tea bags. Cover and set aside to steep for 10 minutes. Combine cornstarch and sugar in a large heatproof bowl. Whisk in eggs one at a time.
2. Remove tea bags; squeeze to extract as much liquid as possible. Whisking constantly, gradually add to cornstarch mixture. Pour back into pan and whisk over medium-high heat until thickened and smooth, 3 to 5 minutes. (Watch carefully to prevent scorching.) Remove from heat and stir in butter and vanilla.
3. Pour pudding into 4 3/4-cup ramekins or bowls. Cover each, pressing plastic wrap directly onto surface, and refrigerate until firm, at least 2 hours. Add a dollop of whipped cream and dust with cinnamon, if desired. Sprinkle with pistachios and serve cold.