Shuffle Up and Deal!
PowerShell v2+, 120 116 114 108 bytes

2..10+[char[]]'JQKA'|%{$z=' '*(8-!($_-10));$x='_'*10;$y=' '*10;" $x 
/$y\
| $_$z|";,"|$y|"*5;"|$z$_ |
\$x/"}


Constructs a range 2..10 and does array concatenation with char-array JQKA. Feeds that into a loop |%{...}. Each iteration, we set $z equal to an appropriate number of spaces (based on whether we're at card 10 or not), set $x to 10 underscores, and set $y to 10 spaces.

Then, we begin our placements. We're going to leverage the default Write-Output to insert a newline between pipeline elements, so we just need to get the stuff on the pipeline. Note that in most places, we're using a literal newline rather than closing and reopening our strings to save a couple bytes.

The first is just $x with two spaces, then $y with two slashes, then the | $_$z|" the pipe, a space, the appropriate number of spaces, and another pipe. This forms the top of the cards up to and including the value line.

We have to semicolon here, since the next uses an array. The ,"|$y|"*5 constructs a string-array, with the comma-operator, of the pipe with spaces - on output, each element of this array gets a newline for free.

Then, the "|$z$_ | for the bottom value marking, and finally $x with slashes for the bottom of the card.

Output Snippet

PS C:\Tools\Scripts\golfing&gt; 2..10+[char[]]'JQKA'|%{$z=' '*(8,7)[$_-eq10];" $(($x='_'*10)) ";"/$(($y=' '*10))\";"| $_$z|";,"|$y|"*5;"|$z$_ |";"\$x/"}
 __________ 
/          \
| 2        |
|          |
|          |
|          |
|          |
|          |
|        2 |
\__________/
 __________ 
/          \
| 3        |
|          |
|          |
|          |
|          |
|          |
|        3 |
\__________/
 __________ 
/          \
| 4        |
...