Place the metal bowl of a stand mixer (or a large metal bowl if you plan to use a hand mixer), as well as the beater(s) in the refrigerator to chill; at least 15-20 minutes.

Toast the coconut by spread in a single layer on a rimmed cookie sheet and baking for about 5 minutes in a 350 degree oven. Watch closely as it can burn quickly. Set aside to cool completely before stirring in the ice cream.

Using a stand mixer with the beater attachment (or hand mixer) beat heavy whipping cream at high speed (start at low and work up to high to avoid splashing); about 3-4 minutes or until stiff peaks form. Stir in coconut milk and sweetened condensed milk until smooth. Gently fold in about 1/2 cup of toasted coconut.

Pour ice cream mixture into 2 8-9" loaf pans or a square cake pan and cover with foil (you could also opt to just leave it in the bowl you mixed it in).

Freeze at least 5 hours or overnight. Let sit for a few minutes on the counter to soften before scooping. Top with additional toasted coconut and lime juice/zest if desired.