Heat a 10-inch cast-iron skillet over medium-high; add 3 tsp. lard. When the lard melts, add 1 cup coconut flakes and cook, stirring constantly, until golden brown, about 4 minutes. Transfer the toasted coconut to a plate.
Wipe out the skillet; heat 1/3 cup lard over medium-high. Remove from heat; let cool 10 minutes. Place the peanut butter in a small bowl and whisk in the lard. Wipe out the skillet. Reserve 1/2 cup of the peanut butter mixture. (You may have a tablespoon or two left to spread on a slice of toast.)
In a medium bowl, whisk the flour, 1 1/2 tsp. sea salt, the baking powder and baking soda. Whisk in the oats. In a large bowl, using an electric mixer, beat the butter, cream cheese and the reserved 1/2 cup peanut butter mixture on low until creamy, about 1 minute. Add both sugars; beat until light and fluffy, about 2 minutes. Add the eggs and vanilla and beat, occasionally stopping to scrape down the sides of the bowl, until blended, about 30 seconds. Add the dry ingredients; beat on low, occasionally stopping to scrape down the sides of the bowl, until just blended. Stir in the toasted coconut. Cover with plastic wrap and refrigerate until chilled, 30 minutes to 1 hour.
Meanwhile, place the skillet in the oven; preheat to 375 degrees. Remove the hot skillet from the oven, add 1 tsp. lard and tilt to coat. Using a rubber spatula, scrape half the dough into the skillet. Carefully (the pan's hot!) press the dough to fill the pan. Sprinkle with 1/2 tsp. salt and more coconut.
Bake until the top is golden and the cookie is just firm in the center, about 15 minutes. Let cool slightly, about 2 minutes. Serve straight from the skillet. Repeat with the remaining 1 tsp. lard, cookie dough and 1/2 tsp. sea salt and more coconut flakes. Or place the remaining dough in a resealable freezer bag and freeze up to 3 months. Let thaw in the refrigerator overnight before baking.