Thanks for contacting "Ask Extension" about your aphid problem. You do not need to treat your garden beds.
Removing the broccoli and tossing the broccoli  was the right move! Next you need to remove nearby weeds where aphids tend to overwinter (especially weeds related to the mustard family). 
To control aphids in your garden:
- Keep a watch on the aphid population next year. Depending on the size of your garden, you  should be able to control them by scraping them off by hand and spraying the underside of the leaves with a strong stream of water.
-Include plants that attract beneficial insects among or near your broccoli plantings. These plants include yarrow, wild buckwheat, white sweet clover, tansy, sweet fennel, sweet alyssum, spearmint, Queen Anne's lace, hairy vetch, flowering buckwheat, crimson clover, cowpeas, common knotweed and caraway.
-You can also introduce natural predators such as lady bugs and green lacewings.  Adult lady bugs that you purchase may fly off, for this reason a better solution is to purchase green lacewing eggs or larvae. 
- If these methods don't work, there are some chemical formulations of neem-oil, capsaicin, insecticidal soaps and essential oil extracts (clove, garlic rosemary) that are OMRI-listed for organic use. Please note that does not mean these sprays are not harmful to bees and other beneficial insects. Look for the "OMRI-listed" label on the product.  Read the label carefully and use as directed.
 I hope this helps,
Happy gardening!
   

Thank you.

Hi again!
I want to make sure I understand your question.  When you say you plan to "clear out the raised bed".  Do you mean that you are removing all the vegetation or are you removing soil as well?
   If you are removing only vegetation,  then your plan is fine.  While the cardboard will inhibit weed growth, it will not break down by spring.  You will need to remove it before planting your crops. Or you can cut holes in the cardboard where you want to plant.
  If you are wanting to create a completely new raised bed, you can use the sheet mulching technique with the cardboard as the bottom layer. Here's a link with more information on sheet mulching (lasagna composting). https://extension.oregonstate.edu/gardening/soil-compost/sheet-mulching-aka-lasagna-composting-builds-soil-saves-time
 

Hi Deb -

You won't completely eradicate aphids, but they should be at a population level you can control.  Be sure you remove nearby weeds around your bed as well as the vegetation you already removed.
  Another protective measure you can do is to place floating row crop covers on top of transplants and  on top of the soil of where you have planted seeds.
  Take care!