Preheat oven to 450°F. Whisk together flour, salt, dry mustard, and cayenne in a small bowl. Bring water and butter to a boil in a medium saucepan over medium-high, stirring to melt butter. Remove from heat; add flour mixture all at once, and stir vigorously until mixture is smooth and thick, like mashed potatoes. Transfer to large bowl, and let stand 3 minutes. Beat dough with an electric mixer on low speed until dough no longer steams and is just warm to the touch, about 1 minute. Add eggs, 1 at a time, beating on medium-high speed until dough is smooth and creamy after each addition. Add cheese, and beat until combined.

Line a baking sheet with parchment paper or a silicone baking mat. Use a 1/2-ounce ice-cream scoop or 2 spoons to portion dough into walnut-size mounds (about 1 tablespoon) 1 inch apart onto prepared baking sheet.

Bake at 450°F for 10 minutes. Reduce heat to 350°F, and continue baking until Cheese Puffs are puffed, deep golden brown, and dry to the touch, 15 to 20 more minutes. (They should sound hollow when tapped on the bottom.)

Cool on baking sheet 3 minutes; split with a serrated knife. Spoon about 1 tablespoon Ham Salad into each, and replace the tops. Serve warm or at room temperature.