Bring milk to a simmer in a medium saucepan over medium heat. Remove from the heat and stir in four tea bags. Cover and steep for 5 minutes.
Strain mixture through a fine mesh sieve into a shallow dish, gently pressing bags to release excess liquid. Stir in 1 tablespoon (15g) sugar, amaretto and 1 teaspoon (5ml) vanilla; set aside to cool.
Meanwhile, whisk together egg yolks, remaining sugar and Marsala in a large, heat-proof bowl. Place bowl over a pot of simmering water and beat on medium-high with a hand mixer or whisk until the mixture has tripled in volume, about 4 to 8 minutes.
Remove the bowl from heat and beat in remaining vanilla, mascarpone and ground tea from the remaining tea bag.
Beat cream until it holds stiff peaks in a medium bowl. Gently fold into mascarpone mixture.
One at a time, dip ladyfingers in batches of 10 into the milk tea mixture to absorb some liquid and soften. Line the bottom of a 9-inch (23cm) glass baking dish with lady fingers and top with a third of the mascarpone mixture, spreading mixture to flatten. Repeating dipping and layers twice, ending with mascarpone mixture.
Refrigerate tiramisu 2 to 24 hours before dusting with cocoa powder and cutting to serve.