In a medium saucepan, combine milk, heavy cream, honey and salt. Bring mixture to simmer, until honey is dissolved. Remove from heat, place tea bags in the mixture and let it steep for 5 minutes. Discard tea bags.
Whisk egg yolks and sugar in a medium bowl until pale, about 2 minutes. Gradually whisk in half of the warm cream mixture, mix until blended. Stir yolk mixture into the remaining cream mixture. Cook over medium heat, stirring constantly, until thick enough to coat a wooden spoon, about 2 to 3 minutes.
Strain custard into another medium bowl, let cool over a bowl of ice water, or chill in the refrigerator, stirring occasionally.
Process custard and food colouring in an ice cream maker according to manufacturer’s instructions. Transfer to an airtight container, cover and freeze until firm, at least 4 hours.
To prepare the caramel sauce, in a heavy saucepan set over low heat, combine the sugar and water and heat just until the sugar is dissolved. Add the butter. Let it come to a boil and cook until it reaches a golden caramel colour.
Remove from the heat and add the cream slowly. Be careful as it will splatter. Whisk to combine and put back on the stove. Let it come to a boil again over low heat and cook 10 to 15 minutes until you reach a nice creamy consistency.
Drizzle the caramel sauce over the ice cream and serve.