In a medium heatproof bowl, place eggs, sugar, lime zest, lime juice, and heavy cream and whisk to combine. Place the bowl over a saucepan of simmering water. Cook on moderate heat, whisking constantly, until mixture becomes thick, about 10-15 minutes.
Remove from heat and immediately strain. Add butter, and whisk until completely melted. Cool completely, then fill the tart crust. Refrigerate the tart overnight. Garnish with additional lime slices, then serve.