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1
Preheat the oven to 400.
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2
Line 2 large baking sheets with parchment paper.
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3
In a medium saucepan, combine the 1/2 cup of water with the whole milk, butter, condensed milk and 1/4 teaspoon of salt and bring to a boil.
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4
Remove from the heat and add the flour all at once; stir with a wooden spoon until a smooth mass forms.
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5
Return the saucepan to the heat and cook over moderate heat, stirring constantly, until the dough pulls away from the sides of the pan and begins to dry out, 4 to 5 minutes.
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6
Transfer the dough to a large bowl and beat at medium speed until cooled slightly, about 1 minute.
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7
At low speed, beat in the whole eggs, 1 at a time, beating until incorporated between additions.
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8
Beat in 1 of the egg yolks until incorporated.
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9
Transfer the dough to a pastry bag fitted with a 1/2-inch plain tip.
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10
Pipe thirty 1 1/2-inch mounds onto the baking sheets, about 1 inch apart.
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11
In a bowl, mix the remaining egg yolk and 2 tablespoons of water.
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12
Lightly brush each mound with the egg wash and sprinkle lightly with sea salt.
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13
Bake for 10 minutes, until puffed and lightly browned.
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14
Lower the oven temperature to 350 and bake the puffs for 20 minutes longer, until golden and crisp.
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15
Let cool on the sheets, then slice each puff in half horizontally.
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16
Line a baking sheet with wax paper.
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17
Working with 6 puffs at a time, fill each puff with the ice cream; replace the tops.
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18
Freeze the profiteroles on the baking sheet while you fill the rest.
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19
Freeze the filled profiteroles just until firm, about 20 minutes.
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20
In a saucepan, combine the coffee, cocoa powder, sugar, corn syrup and 1/4 teaspoon of salt; whisk until smooth.
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21
Bring to a boil, whisking constantly.
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22
Remove from the heat and whisk in the chocolate, butter and coffee liqueur.
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23
Transfer the sauce to a pitcher.
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24
Transfer the profiteroles to plates.
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25
Drizzle with the mocha sauce and serve.
