Preheat oven to 375 degrees. Coat a standard muffin tin with non-stick cooking spray, or line with paper muffin liners; set aside.
In a medium bowl, mix together flour, oats, baking powder, cardamom, baking soda, and salt.
Pour melted butter to a separate, large bowl. Add sugar and whisk until well combined. Mix in milk, grated apple, eggs, and vanilla.
Gently stir dry ingredients into the wet until a batter forms. Fold in 1/2 cup chopped pecans until well incorporated, being careful not to over mix the batter.
Fill muffin cups about 3/4 with batter and sprinkle with remaining 1/2 cup chopped pecans, dividing the nuts evenly among the muffins. Bake until the tops are golden brown and a toothpick inserted into the center comes out clean, about 25 to 27 minutes. Remove from oven and allow muffins to cool in the tin for about 10 minutes before transferring them to a wire rack to finish cooling.
Serve warm or at room temperature. These muffins will keep for 2 days stored on the counter in an airtight container. You can also freeze them for up to three months (they will defrost on the counter overnight, in the oven, or microwaved in 10-second intervals).