How can I control how many passes (depths of cut) my toolpath will take?

In most toolpaths you can set a Pass Depth for the selected bit. The program will create enough passes until it gets to the Cut Depth set for that toolpath.

The Profile toolpath in Aspire and VCarve Pro can be modified by the program as explained in this excerpt from the Help document:

By default, the program can modify the precise step down by up to 15% in either direction, if by doing so it is able to reduce the total number of passes required to reach the desired cut depth. If this is unacceptable, Aspire and VCarve Pro users can use the Edit Passes feature described below.

Therefore, Aspire and VCarve Pro have an additional feature in the Profile Toolpath that lets you precisely set up the number and depths of each pass. You would open that option by selecting Edit Passes on the Profile toolpath form and filling out the appropriate section. The Help Contents or Reference Manual discusses this in detail and would a good source of information.

Tip: The ability to Edit Passes and quickly assign different pass depths is a quick way to leave an 'onion skin' to be removed by a final pass. It also provides a quick way to adjust Profile toolpaths using bits such as v-bits and ball nose bits where the amount of material removed would increase with each pass if a constant Pass Depth was set.