Place 2 sheets of parchment paper on a counter or flat surface. Set aside.
In a large nonstick pot or deep skillet, melt butter over medium heat.
Stir in sugar and 1/2 cup milk until combined.
Add in cream of tartar just when mixture begins to bubble slightly.
Bring to a rolling boil and as soon as it comes to a roiling boil continue cooking for 2 MINUTES while stirring constantly. See note.
Remove from heat.
Stir in peanut butter and vanilla extract.
Add half of the oats and stir until well combined.
Stir in just enough of the remaining milk to create a thick and creamy batter. (may not need all of the milk)
Stir in remaining oats.
Working quickly, drop batter by the spoonful onto the parchment paper. Make them as big or as small as you'd like.
Let the cookies sit for 20-30 minutes to set.
Once set, wrap individually in plastic wrap and store in an airtight container.