As others have said, you're going to have to write
Test2.Subroutine(Test.AnObject)
This is a good example of why it's worth being a little careful with the With construct in VB.Net. My view is that to make it worth using at all, you really need to be setting more than one or two properties, and/or calling more than one or two methods on the object in the With statement.
When there are lots, and you're not interspersing the .SomeProperty = , or .DoSomething, with other things, it's a terrific aid to readability.
Conversely, a few dots sprinkled amongst a load of other stuff is actually a lot harder to read than not using With at all.
In this case, . characters on their own could easily get lost visually, although of course, it would be syntactically consistent.
I guess they just chose not to implement it. VB isn't really the sort of language where they want to encourage single character language elements, and as a heavy user of VB.Net, I broadly agree with that.
Bottom line: if you're using a With clause with many contained elements, having to refer to the object itself isn't that big a deal. If you're using it with just one or two, maybe better not to use a With clause in the first place.