In a large stock pot, combine heavy whipping cream and whole milk. Heat over medium-high until bubbly and steaming.
Add vanilla and coffee extracts as well as espresso powder. Stir to combine and remove from heat.
In a large bowl, whisk together 5 egg yolks, sugar, and salt until it's pale, thick, and creamy.
Slowly ladle in a spoonful or two of hot milk mixture to temper the eggs, constantly whisking to combine.
Pour tempered egg mixture into the pot of milk and stir to combine. Add your chopped chocolate and cocoa powder and whisk until melted and smooth.
Cook over medium-high heat until custard thickens to a loose pudding consistency. Remove from heat.
Strain ice cream mix through a fine-mesh sieve into a large heat-proof bowl. Cover and let chill completely.
Churn ice cream base in an ice cream maker until very thick and creamy. Remove from bowl and mix in half your raspberries.
Scoop ice cream to serve and garnish with more raspberries and fresh basil.