Electronic – EEPROM in beaglebone black

Simple enough. Pins 1 is the SPI Chip Select (GPIO). 2 - 4 are SPI data and clock pins. RST is an active low input (to the ENC28J60) so any GPIO can be used. INT and WOL are active low outputs (from the enc), so a GPIO in input mode on the BeagleBone.

For the SPI pins, you want the p9 header pins 28-31, which are Chip Select, Data Out, Data In, Clock. Any GPIO will work for the other signals.

You could calculate it by reading the EEPROM datasheet and adding up the time take to transfer all the bits as Ignacio Vazquez-Abrams suggested in a comment. Because you've already selected a device and have it working though you might find it easier just to measure it. Normally I'd do something like the following and use a scope to measure it:

// Take an I/O pin high
x=do_eepromread();
// Take the I/O pin low

If you don't have a scope you could enclose the reading in a loop and maybe turn a LED on and off with something like this:

uint32_t i;
// Turn on LED
for (i=0; i < 100000; i++)
    x=do_eepromread();
// Turn off LED

Depending on how many bits are transfers the second piece of code will probably take something like 30 seconds or so which you should be able to measure reasonably accurately with a stopwatch and then divide by 100,000.

Both those methods will introduce some error because of the time to toggle an I/O line and in the latter case the the loop delays, but I think for your purposes they should be near enough and you might find it easier than trying to calculate it exactly.