Preheat oven to 425 degrees.with a rack in the center. Line two unrimmed baking sheets with parchment paper or Silpats (French nonstick baking mats).
Fill a pastry bag fitted with a 1/2-inch (Ateco No. 806) tip with pate a choux batter; pipe out oblong shapes, about 3 1/2 inches long and 1 inch wide, onto prepared baking sheets at 2-inch intervals. Gently run a fork dipped in water along each top, making straight lines to ensure even rising.
Cover one baking sheet with lightly oiled plastic wrap, and place in refrigerator. Transfer the second sheet to the oven. Bake 10 minutes; reduce oven temperature to 350 degrees. Bake until golden brown, 25 to 30 minutes more. Turn off oven; prop door open slightly to let steam escape. Allow eclairs to dry in oven until centers are damp but no wet dough remain (test by cutting into the center of one), about 15 minutes. Transfer to a wire rack to cool slightly. Raise heat back to 425 degrees and repeat process with remaining batch. If serving immediately, fill eclairs while still warm so they can take more cream; if filling at a later time, insert a skewer into one end, and move it around to expand opening for cream; set aside.
Transfer pastry cream to the bowl of an electric mixer fitted with the paddle attachment. Beat until smooth and softened. Fill a pastry bag fitted with a coupler and filling tip (Ateco No. 230) with pastry cream. Insert tip into one end of each eclair; fill.
To make the glaze, heat cream in a small saucepan. Pour over chocolate in a small bowl. Let stand until chocolate is melted, stir until smooth. Dip top of each eclair into glaze; let excess drip off before turning over. Transfer to a wire rack to allow glaze to set. Serve, or store in an airtight container in the refrigerator up to 1 day.