TO MAKE THE CRÈME ANGLAISE: In a large bowl, whisk together egg yolks, sugar, cornstarch and salt until thick and pale, 2 to 3 minutes.

In a medium saucepan, bring milk to a boil over medium heat; remove from heat. In a slow and steady stream, whisking constantly, add about 2 tablespoons hot milk to egg mixture, then whisk in remaining milk. Transfer back to saucepan and cook over medium-low heat, stirring constantly with a wooden spoon, until custard is thickened and registers 175° (do not let boil), about 5 minutes. Beat in vanilla.

Transfer to 1 or 2 serving bowls. 
 

TO MAKE THE SPAETZLE: Into a large bowl, sift all-purpose flour, chestnut flour and granulated sugar. Add whole eggs, egg yolks, milk, butter and salt; whisk until smooth.
 

Heat about 2 inches oil to 375° in a 4- to 5-quart heavy pot over medium-high heat. Reduce heat to low. Working carefully over oil, use heatproof spatula to force about  2 tablespoons batter through spaetzle maker, food mill or colander, frying spaetzle until golden and puffed, about 45 seconds.

Using a using slotted spoon, transfer the fried spaetzle to paper towels to drain.

Transfer warm spaetzle to a serving plate and immediately sprinkle with sugar. Repeat with remaining batter.

Serve spaetzle with Crème Anglaise.