Melt together baking chips and heavy cream in microwave, stirring every 20 seconds. Stir in vanilla bean paste and extract. Set aside to cool.
In the top of a double boiler over simmering water, whisk together eggs, sugar, cream of tartar, and salt until it reaches 160 degrees. Remove from heat.
Whisk cooked mixture in a stand mixer, on high speed until cooled to the touch. It will look like thick marshmallow cream. Reduce to medium speed, gradually beat in butter, a few tablespoons at a time, until smooth. Beat in cooked white chocolate mixture.