Make the muffins
Position a rack in the center of the oven and heat the oven to 350°F. Lightly oil (or spray with cooking spray) the top of a standard 12-cup muffin tin (cups should be 2-3/4 inches across and about 1 inch deep) and line with paper or foil baking cups.
In a large mixing bowl, sift together the flour, baking powder, baking soda, and salt; mix well. In a medium mixing bowl, whisk together the sugar, butter, milk, crème fraîche or sour cream, eggs, and egg yolk until well combined.
Pour the wet ingredients into the dry and fold gently with a rubber spatula just until the dry ingredients are mostly moistened (the batter will be lumpy). There should still be quite a few streaks of dry flour.
Sprinkle the pineapple and coconut onto the batter, and fold them in until just combined. (The batter will be lumpy; don’t try to smooth it out.) Do not overmix.
Use an ice cream scoop if you have one with a “sweeper” in it; otherwise, use two spoons to spoon the batter into the muffin cups, distributing all of the batter evenly. The batter should mound higher than the rim of the cups by about 3/4 inch. Bake until the muffins are golden brown and spring back lightly when you press the middle, 30 to 35 minutes. (The muffin tops will probably meld together.) Let the tin cool on a rack for 15 to 20 minutes.
Glaze the muffins
Put the confectioners’ sugar in a small mixing bowl. Add the pineapple juice and whisk until smooth. The glaze should be thin enough that it will drip off a spoon; if it’s more like a spreadable icing, thin it with more pineapple juice, 1 Tbs. at a time.
When the muffins have cooled down but are still slightly warm, use a table knife to separate the tops, and then invert the pan and pop out the muffins. Put the muffins on a rack over foil to catch any glaze that drips off. Dab the glaze on the muffins with a pastry brush, or spoon the glaze on and let it drip over the sides. It should leave a smooth, somewhat translucent coating. You may not need all of the glaze. Wait 20 to 30 minutes for the glaze to set; it won’t dry completely.
Photo: Scott Phillips