Bring the cream to a simmer and pour over the chocolate in a heatproof bowl. Let sit until the chocolate begins to melt, about 1 minute, then stir until smooth. Beat in the butter and liqueur until thoroughly combined. Cover and chill for at least 2 hours.
Scoop the chocolate mixture with a mini ice-cream scoop or a teaspoon and roll into 1-inch (approximately 1 ounce) balls, powdering with your hands with confectioner’s sugar if necessary to keep the chocolate from sticking. Place on a baking sheet lined with parchment paper and freeze for at least 2 hours.
Prepare three shallow bowls: one with beaten egg, one with flour, and one with shredded coconut. Roll the frozen balls in each bowl: first in the egg, then in the flour, then in the egg again, and finally in the shredded coconut.
Let the balls rest for a few minutes in the refrigerator, then dip them again in all three bowls in the same order. Freeze the double-dipped balls for at least 1 hour.
In a deep pan, heat the vegetable oil to 375 degrees F. Carefully fry the truffles, working in batches so as not to crowd the pan, until golden brown, about 2 minutes. Serve hot.