In a small saucepan, combine 2 cups water, the sugar, and jalapeño. Bring to a simmer, stirring, until the sugar is dissolved. Remove from the heat and let cool. (The longer you let the mixture stand, the hotter it will get from the jalapeño. I left mine for about 45 minutes.) Strain into a pitcher, discarding the jalapeño.

Meanwhile, puree the strawberries with the remaining 2 cups of water in a blender. Pour through a fine mesh sieve into the pitcher, pressing on the solids with a wooden spoon to extract as much liquid as possible. (You should have just over 2 cups.) Add the lime juice to the pitcher and stir to combine. Chill in the refrigerator.

For each drink, fill a glass with ice. Add about 1/4-1/3 cup of the strawberry lime jalapeño mixture and top with beer.