Preheat the oven to 325 degrees Fahrenheit. In the bowl of a stand mixer fitted with the whisk attachment, beat together the egg yolks and sugar at medium low speed until the mixture lightens in color to a pale gold, stopping to scrape down the sides and bottom of the bowl as-needed, about two minutes.
Switch to the paddle attachment, and with the mixer going at low speed, add the coconut milk. Then add the lime juice, then lime zest and optional food coloring and mix until combined, scraping down the sides of bowl as-needed. Tap the bowl on counter to release any air bubbles, then place the crust on lipped baking sheet and pouring the filling into the crust. Bake at 325 until the filling is juuust set, about 25 to 30 minutes. Remove and allow to cool to room temperature.
While the syrup is boiling, beat the egg whites in the bowl of a stand mixer fitted with the whisk attachment at medium high speed until there's little bubbles at the top of the egg white mixture. Add the cream of tartar, then continue beating at medium high speed until soft peaks form. Stop the mixer until the syrup has reached the right temperature.
For a more rustic look, simply spoon the meringue on top of the cooled tart. For a more polished look, add the meringue to a piping bag fitted with a medium star tip and pipe the meringue onto the surface of the lime tart in small star shapes + larger rosette swirls. Use a kitchen torch to "toast" the meringue until lightly golden at the tips, then place the tart in the refrigerator for at least 6 hours (overnight works best) before serving. Keep chilled.