Beat the softened butter, sugar, egg, and vanilla until creamy, using handheld mixer. Scrape down the bowl as needed to incorporate ingredients evenly.
Add banana and beat until smooth.
Add pineapple, orange (or clementine) zest, and beat on low speed until combined.
Stir together flour, salt and baking soda in a separate bowl. Add dry ingredients into the butter mixture. Beat at low speed until a soft dough forms.
Stir in 3/4 cup of the white chocolate chips (about half of them). Cover the bowl and chill the dough in the refrigerator for about 30 minutes, or until you can roll it into a ball without it sticking to your hands.
Preheat oven to 325 degrees. Line two cookie sheets with baking parchment. Roll dough into 1-inch balls, and distribute evenly on cookie sheets about 2-inches apart. Using your palm, flatten the balls of dough slightly.
Place about 3 white chocolate chips into the flattened dough balls.
Bake for 10-11 minutes. The cookies may only spread slightly during baking — that’s okay.
Allow cookies to cool on the warm cookie sheet for a few minutes. Transfer to a cool sheet or wire rack to cool completely.