Meanwhile, in a medium heatproof bowl, using an electric mixer, beat the egg yolks at high speed until thick, about 3 minutes. Add 1/4 cup of the granulated sugar and beat until very thick, about 5 minutes. At low speed, gradually beat in the warm half-and-half. Fill the saucepan with 1-inch of water and bring to a simmer. Set the bowl with the egg yolks over the simmering water and cook, stirring constantly, until thickened and an instant-read thermometer inserted in the yolks registers 170°, about 9 minutes. Add the softened gelatin to the custard and cook for 1 minute, stirring until dissolved. Remove the bowl from the pan. Stir in the pureed sweet potatoes, 2 teaspoons of the vanilla, the pumpkin pie spice and the salt.