Make the jalapeño tequila. Place the sliced jalapeño in a jar with the tequila. Refrigerate for 24 hours, then strain out the jalapeño and seeds.
Make the rhubarb mint syrup. In a small saucepan over medium-high heat, combine the rhubarb, mint, water, and sugar. Bring to a boil, then reduce to a simmer and cook until the rhubarb is soft, about 15 minutes. Let cool, then press through a fine-mesh strainer. Store refrigerated in an airtight container for up to 2 weeks.
Make the cocktail. In a cocktail shaker, combine the infused tequila, lime juice, and rhubarb syrup. Fill the shaker with ice and shake vigorously for 15 seconds.
Place a thin layer of kosher salt on a small plate. Dampen the rim of a cocktail glass with lime juice and dip into the salt. Fill the prepared glass with fresh ice. Using a cocktail strainer, pour the mixture over the ice. Garnish with a lime slice, rhubarb slices, or mint leaves, if desired.