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1
Preheat the oven to 400F.
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2
Bring the butter, salt, and 1 cup water to a boil in a large, heavy saucepan over medium heat, stirring occasionally (the butter will melt).
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3
Add the flour; stir vigorously until incorporated.
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4
Continue to cook, stirring, until the mixture pulls away from the sides and a thin film forms on the bottom of the pan, 1 to 2 minutes.
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5
Remove from heat; let cool 5 minutes.
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6
Transfer the dough to a large bowl; add the eggs, one at a time, beating with a wooden spoon to incorporate each egg before adding the next, about 2 minutes.
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7
Stir in pepper, ham, and shredded cheese.
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8
Spoon dough into a pastry bag fitted with a 1/2-inch star tip.
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9
On a baking sheet lined with a Silpat baking mat or parchment paper, pipe 1 1/2-inch-wide rosettes, 1 inch apart.
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10
Make a deep indentation in the center of each with your thumb (dampen the thumb to keep it from sticking to the dough).
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11
Bake until crisp and golden, 25 to 30 minutes.
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12
Transfer thumbprints to a wire rack to cool completely.
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13
Press a cheese cube into center of each.
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14
Place on clean baking sheets; freeze (uncovered) until firm, about 1 hour.
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15
Transfer to an airtight container; freeze until ready to use, up to 6 weeks.
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16
To serve, preheat the oven to 425F.
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17
Place the thumbprints on ungreased baking sheets; bake until heated through and cheese is melted, 10 to 14 minutes.
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18
Serve warm.
