Hi,
You will need to follow the steps below
1. create an Option (Administration > Platform > Options) with a high Date i.e 01/01/1900 (this is done to get full extract the first time you run the workflow. If you do not want this set this time from when you want the extract to begin, say the name of the options is 'broadlogExtractTime'

2. In your workflow add the Javascript Activity to initialize the variable and add the following script below:
vars.endTime = formatDate(getCurrentDate(),'%4Y/%2M/%2D %2H:%2M:%2S');
vars.startTime = formatDate(getOption('broadlogExtractTime'),'%4Y/%2M/%2D %2H:%2M:%2S');
3. Add a query Activity after the Initialization JavaSrcipt Code and filter by last modified date like shown below

To add these variables you will need to use the expression editor in the Query activity and add the expression in the following format
$datetime(vars/@startTime) and $datetime(vars/@endTime)
4. Last and the most important step is to update the Option to capture the successful increment of the extract. Add an End activity and in the Advanced tab add the script below:
setOption('broadlogExtractTime',vars.endTime);
Congratulation!!! you have set up an incremental extract of the delivery logs.
Thanks,
Pulkit