Combine whole milk and coconut milk together in a small saucepan. Heat gently over low-medium heat until almost at a simmer. Add in the Earl Grey tea bags and remove from heat. Let it steep for 10 minutes.
In a medium glass bowl, add the egg yolks, sugar, flour, cornstarch, salt, and vanilla extract. Whisk everything together.
Use a spatula to gently press on the Earl Grey tea bags to extract as much tea and remove the tea bags.
Return the tea-steeped cream onto the stove and turn the heat back onto medium. Heat the cream until it's almost at a simmer.
While whisking the egg mixture, gradually drizzle in the hot tea-cream as to not scramble the eggs. This is known as tempering the eggs.
When all the cream has been added to the eggs, pour the mixture back into the saucepan and continue to whisk until the cream begins to thicken, about 5 minutes over low-medium heat.
Once thickened, remove the pastry cream, stir in the bergamot oil and chill over an ice bath.
Transfer to a clean bowl and place a piece of plastic wrap over top of the pastry cream. Chill in the refrigerator for at least 1-2 hours.