To prepare the ice cream, in a medium saucepan, combine milk, heavy cream, 1/4 cup sugar, salt and espresso powder. Bring mixture to simmer, until sugar is dissolved. Remove from heat and set aside.
Whisk egg yolks and remaining sugar in a medium bowl until pale, about 2 minutes. Gradually whisk in half of the warm cream mixture, mix until blended. Stir yolk mixture into the remaining cream mixture. Cook over medium heat, stirring constantly, until thick enough to coat a wooden spoon, about 2 to 3 minutes.
Strain custard into another medium bowl. Let cool over a bowl of ice water, or chill in the refrigerator, stirring occasionally.
Process custard in an ice cream maker according to manufacturer’s instructions. Transfer to a 9 x 13-inch baking pan, level the top, cover and freeze until firm, at least 4 hours.
To prepare cookie dough, sift the flour and salt in a large bowl. Mix in pecans. Set aside.
Mix espresso powder and hot water until the powder is completely dissolved.
Cream butter and powdered sugar in a bowl of a standing mixer until light and fluffy.
Beat in the espresso mixture.
Reduce the speed to low and beat in the flour mixture until just incorporated.
Gather dough and form a dish. Cover with plastic wrap and refrigerate for about 30 minutes to chill.
Preheat oven to 350F. Line 2 baking trays with parchment paper.
On a lightly floured surface, roll out the dough to 1/4 inch thickness. Cut into 3-inch rounds using a floured cookie cutter. Place on the prepared baking sheets and place in the refrigerator for about 15 minutes.
Bake the cookies for 8 to 10 minutes, or until cookies are lightly browned.
Remove from oven and let the cookies cool a few minutes on the baking sheet before transferring them to a wire rack to cool completely.
To assemble the sandwiches, remove ice cream from the freezer, use a cookie cutter to cut out a disc of ice cream and place it on top of one cookie. Place another cookie on top of the ice cream. Lightly press to adhere the sandwich.
Serve immediately. Or wrap each sandwich with plastic wrap and place them in the freezer.