Heat milk in large saucepan until small bubbles appear around edge. Beat yolks and sugar in bowl until pale yellow and thick, 3 minutes. Beat in flour. Gradually beat in hot milk. Pour back into saucepan. Cook, stirring, over medium-high heat until mixture comes to boiling and thickens. Lower heat; cook, stirring, 2 minutes, until very thick (mixture will be lumpy in beginning, but lumps will disappear). Remove from heat. Stir in butter and vanilla until butter is melted. Place waxed paper directly on surface. Refrigerate at least 2 hours. If too stiff, gradually stir in 2 to 4 tablespoons heavy cream or milk, a tablespoon at a time. Makes about 3-1/2 cups filling.
Heat water, butter, sugar and salt in saucepan to full, rolling boil. Add flour all at once; stir vigorously with wooden spoon until mixture forms thick, smooth ball that leaves sides of pan clean, about 1 minute. Continue to cook, stirring, for another 2 minutes. Remove saucepan from heat. Add eggs, one at a time, beating well after each addition with wooden spoon for 30 seconds or until shiny and smooth. Makes enough batter for 12 eclairs.
Heat oven to 425°F.
Attach large plain tip to pastry bag (or use bag without tip); spoon dough into bag. Press dough out into 4- or 5-inch-long strips, 1 inch wide, on ungreased baking sheets, spacing 1-1/2 inches apart. Or shape with spoon in 4 x 1-inch strips.
Bake in 425°F oven 35 minutes or until puffed and golden brown. Turn oven off; let eclairs sit in oven, with door slightly ajar, 10 minutes. Transfer eclairs to rack to cool.
Make small hole in one end of each eclair with tip of knife. Fit pastry bag with small plain tip. Fill bag with custard filling. Press filling through hole into eclairs. Or split eclairs lengthwise, then spoon filling in, and replace tops.
Mix chocolate, butter and water in small bowl. Place in pan of barely simmering water; stir often, to melt chocolate. Remove from heat. Stir in sugar and vanilla. Spread over eclairs while still warm. Let stand until glaze is firm. If desired, drizzle melted white chocolate over tops.