Preheat the oven to 350°F. Line a baking sheet with parchment paper.
In a blender or food processor, pulse 1 cup oats 5 times, or just until the oats are broken.
In the bowl of a stand mixer fitted with the paddle attachment, cream 3/4 cup butter, 1 cup brown sugar, and 1/2 cup granulated sugar until pale and smooth. Mix in 2 eggs, 2 teaspoons vanilla, and 1/4 cup molasses until combined.
Add 1 cup flour, 3/4 teaspoon salt, 1 teaspoon baking soda, 1 teaspoon baking powder 1 teaspoon cinnamon, 2 teaspoons ginger, and 1/2 teaspoon cloves. Mix just until combined. Then mix in the remaining 1 1/4 cup flour, pulsed oats, and remaining 1 cup oats.
Use a medium cookie scoop to scoop dough onto the prepared baking sheets. Bake for 10 - 12 minutes, or until the edges are just light golden brown. Take them out a little early for softer cookies and bake a little longer for crispier cookies.
Let cookies rest on pan for 2 minutes and then transfer to a cooling rack. Allow cookies to cool completely.
Whisk together the 2 cups powdered sugar, 1/2 teaspoon vanilla and 2 Tablespoons milk in a bowl. If it's thick, add the last Tablespoon milk. Then drizzle glaze on each cookie. Allow to set until harden.
Notes
Freezer instructions: Cool cookies completely and then place in a freezer bag or an airtight container. Freeze up to 3 months. Remove from the freezer 1 hour before ready to serve, or eat frozen. You can also warm in the microwave for 10 - 15 seconds.Storage: Store in a covered container at room temperature up to 3 days.