Combine the water and tea in a medium saucepan, bring to a boil, and then turn off the heat and let steep for 5 minutes. Use a fine mesh strainer or cheesecloth to strain the liquid over a large bowl; discard the tea leaves.
Transfer the liquid back to the saucepan and bring to a boil, then decrease the heat to a simmer. Add the salt, sugar, butter, and half-and-half and whisk until the butter has completely dissolved and a little foam forms on the surface. Serve the tea in small bowls.