The most common blocks lumped into a "various" category by brokers are shares bought from a dividend reinvestment program. Look for smaller blocks often with less than 1 share in them. These are the ones being aggregated. Remember to differentiate between long-term and short-term blocks.
If you sum your cost basis for these blocks and it is the same as the amount listed for "various" on your 1099, just enter the amounts listed in the tax printer as your cost basis into the field for the broker cost basis.
If your records and the broker disagree, see the info below.

There are at least 2 fairly simple ways to do this.

Divide the difference between the broker's cost  information and your records among all the blocks lumped together as "various".
For example broker says cost basis is 125 for 5 blocks of stock. Your records indicate the cost basis is 120.
In this example, [Broker info] - [Your info] = 5.
Divide this amount among all the blocks. In this example, that leaves each block with 1 added to your cost basis information. In the tax printer your cost basis information is displayed next to the field for entering the broker information. Just add 1 to the cost basis amount displayed and enter it in the field for the broker information.
This will mean all these transactions will appear on a form 8949.
 

A second method will decrease the number of transactions on the 8949 and still give accurate information.
First calculate the difference in cost basis in your records and the broker's.
As before [Broker info] - [Your info] = adjustment amount.
Instead of allocating this equally among all the blocks, allocate it only to one block. Usually, you would choose the block with the highest cost basis in your records. Using the same scenario used above, the adjustment is $5.
For all the blocks except one enter the same amount in the broker information field as is displayed as the amount from your records. For the one exception increase or decrease the cost basis amount you enter by the adjustment amount. So from the example above, you would add 5 to your cost basis information and enter the result in the broker cost basis field. You total gain will remain the same.
This method has the advantage that all the blocks you kept the broker and your numbers the same do not need to be printed on the 8949. They will be added to a summary line on Schedule D only.