Lightly crush the cinnamon sticks, cardamom pods, cloves, and peppercorns with the side of a knife or the bottom of a small pan. The spices should crack open without being ground into powder.

Add the water, crushed cinnamon, cardamom, cloves, peppercorns, and sliced ginger to a 2- to 3-quart saucepan.

Set the saucepan over medium-high heat and bring the mixture just to a boil. Reduce the heat to low so the liquid maintains a gentle simmer.

Cover partially and simmer for 10 minutes. The liquid should become golden-brown and smell strongly of cinnamon, ginger, and cardamom.

Stir in the brown sugar until completely dissolved, about 30 seconds.

Remove the saucepan from the heat: Add the tea bags or loose tea, cover, and steep for 5 minutes. Avoid steeping much longer, as strong black tea can become noticeably bitter.

Lift out the tea bags without aggressively squeezing them. If using loose tea, leave it in place until the concentrate is strained.

Stir in the vanilla extract: The concentrate should taste intentionally strong and slightly sweeter than a finished cup because it will be diluted before serving.

Pour the mixture through a fine-mesh strainer into a heatproof measuring cup or bowl. Discard the spices, ginger, and loose tea.

Let the concentrate cool at room temperature for about 30 minutes, or until it is no longer steaming.