Combine sugar, water, and 1 tablespoon coarsely ground black pepper in a small saucepan and bring to a simmer. Simmer until sugar fully dissolves, stirring; this takes about 1 minute. Cool completely. Strain syrup and discard black pepper.
Make drinks:
Muddle strawberries a medium-sized jar. Add lime juice, ½ cup of cooled syrup, and tequila and stir to combine.
To finish:
Swipe rims of 2 rock glasses, mason jars, or equivalent 11 or 12-ounce glasses with lime. Combine 1 tablespoon sugar, ¾ teaspoon finely ground black pepper, and salt in a shallow plate and dip rims in it to coat them. Carefully fill glasses with ice. Divide strawberry-tequila mixture between glasses, including the muddled strawberries.