COmpost

I often do that with soft leaved plants (Google chop & drop composting) but I think you've chosen the 2 worst things to do it with  Brassica and sweetcorn stems take a really long time to rot away. I tend to put them in a pile against my back fence where I can simply forget about them altogether   

I'm glad you told us that Mum because i stripped the leaves of the brassicas and put the storks on a separate heap with the sweet corn storks so when there  dried out we can burn them along with other weeds that won't compost is that rite 

The reason we make a compost heap on a limited part of our ground is for the following reasons:
1.   materials rotting in a heap take nitrogen to do so and this does not deplete nitrogen from the soil
2.   materials rot better when different materials are mixed together
3.   the heap attracts specialist workers who are more effective than ordinary soil creatures
4.   rotting in situ works against rotation of crops
5.   the compost produced can be targeted to where it is most advantageous , eg under the roots of transplanted brassicas
6.   the process is much speedier than composting separately
7.   the material is of much better quality and of smaller particle size so that it can be more easily absorbed by both plants and soil
8.  the composting process can be adjusted for maximum effectiveness by incorporating water and kitchen waste which quickly produces heat
9.  the composting process produces heat which can kill both weed seeds and pathogens
All weeds can be composted if necessary by firstly either drying or wetting potentially troublesome materials in a bucket prior to adding to the heap.   A very few weeds are potentially dangerous such that the benefits of producing compost is likely to prove less beneficial than the dangers of spreading these weeds to areas hitherto unaffected by them such as ground elder or horsetail/marestail.

I do the bash and put in the compost heap method. If any large lumps are still there when I come to use the compost, I chuck them back in the heap with the next lot of stuff.

As others have said, if you can shred them or cut them up fine, they rot much faster.

File and forget in a corner is also an option.  Even the most unpromising heap of woody waste will rot in the end and does so faster if you can cover it with something.  Split open compost bags and bricks, tarpaulin, ... whatever you have to hand