Fill a large bowl with ice and a little water and set aside.
Combine the heavy cream, vanilla paste and 1 tablespoon of the sugar in a small saucepan. Bring to a boil over medium-high heat, stirring occasionally, then reduce the heat to a simmer.
Combine the egg yolks with the remaining 2 tablespoons sugar. Add the yolks and sugar to the hot cream mixture and cook, whisking constantly, until slightly thickened, about 3 minutes. Continue cooking, undisturbed, until the sauce coats the back of a spoon, about 2 minutes.
Pour the mixture into a blender and blend until completely smooth and no lumps remain. Pour the sauce into a medium heatproof bowl and place that bowl in the prepared ice bath. Stir continuously to chill the creme anglaise, about 2 minutes.
Divide the berries among 4 serving bowls. Spoon the creme anglaise over the berries.