To make jalapeno simple syrup mix one cup water with one cup sugar and bring to a gentle simmer on the stove, add in 1/3 cup of sliced (with seeds removed) jalapenos to the sugar & water. Cook on low for 15-20 minutes. Let cool completely. Store in an airtight jar or container in the refrigerator.
To make peach puree, add peach slices and the peach syrup to a blender. Cover and blend 20 seconds or until smooth and fully combined.
To a cocktail shaker, add 5 TBL peach puree, the tequila, lime juice, jalapeno syrup, and triple sec. Add 1 cup of ice to the shaker, cover, and shake about 10 times.
Rim a drinking glass with the juiced lime. Place the chile-lime seasoning on a small plate and dip the rim of the glass in the seasoning to lightly coat. Carefully fill the glass with ice.
Using a cocktail strainer, pour the peach margarita into the glass. Top with 4 dashes of peach bitters, and garnish with a fresh jalapeno slice.