Since making the mocha crepes is the most time consuming step in this dessert recipe, you may want to use the make-ahead directions. To show off the white chocolate filling, serve the crepes on a pool of the raspberry sauce.
Combine flour, cocoa, sugar, espresso powder, baking powder and salt in medium-size bowl. Add milk, butter, eggs and vanilla; beat on low until blended; beat at medium-low just until smooth.
Coat 8-inch nonstick skillet with cooking spray. Heat over medium heat until drop of water sizzles. Pour 2 heaping tablespoons batter into skillet and rotate skillet until film of batter covers bottom. Cook until surface of crepe begins to dry, 2 to 3 minutes. Run spatula around edge to loosen. Turn over; cook until bottom is light brown, about 2 minutes. Remove crepe. Repeat with remaining batter, stacking crepes between sheets of waxed paper and covering (see Note).
Bring cream to boiling in heavy medium-size saucepan over medium-high heat. Remove from heat. Stir in chocolate until melted and smooth. Stir in liqueur. Pour into bowl, straining through sieve. Refrigerate 30 minutes, stirring occasionally.
Using whisk or electric mixer, beat chocolate mixture just until fluffy, 30 seconds. Refrigerate until chilled, about 1 hour. Then beat until thickened, about 30 seconds (do not overbeat). Fold in mini chips. Refrigerate.
Press berries through fine sieve into small saucepan; discard seeds. Stir in cornstarch; simmer, stirring, until thickened, 1 to 2 minutes. Refrigerate.
Spread about 3 tablespoons ganache along center of each crepe. Overlap sides. Spoon 1 tablespoon puree onto each serving plate; top with a filled crepe.
Crepes can be made ahead. Stack with waxed paper between them; wrap in plastic. Refrigerate several days, or freeze up to 1 month. To use, thaw unwrapped at room temperature for 3 hours.