I bake these cookies every day but with varying results. It's a simple recipe where flour sugar and oats are combined and hot butter with baking soda are added. I sometimes add a little shortening to the dough. Today the butter solids got too hot and burnt the bottom of my saucepan while I heated the butter so I'm assuming the quantity of butter was reduced a little. I'm not too experienced a baker but I bake these for my restaurant very frequently.
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With the information you have provided I would guess that you are getting 'crumbling' because you have insufficient fat in your recipe (or are loosing some to the your process). Make sure your volume and temperature of melted butter is consistent. You will also want to let your melted butter cool slightly before adding it to dry stuff (after melting let your butter rest till it is below 130°F(55°C). If these are still 'too crumbly' increase the amount of fat. Not all fats are created equal here. If your recipe does not include egg (at all) then I would bump the butter by 1 tablespoon (up to one half the current measure of butter) If there is already 'some egg' start with adding one additional egg YOLK (no more white).
Consistency is going to be the most important part of addressing this issue. In the kitchen insanity is doing something different and expecting the same results.