Originally from July/August ’06 Cooks Illustrated, with additional notes.

Brine:
6 cups water
3 cups sugar
2 cups table salt
2 garlic heads crushed
4 cups orange juice

Take 7-8 pound picnic shoulder (our grocery store called it Pork
Picnic), cut 1″ deep and wide slits about 2″ apart, then brine in the
above for 18-24 hours (for the family meal, we did closer to 30 because
of work scheduling, we previously did 12 and that also worked).

Paste:
12 cloves garlic, chopped
2 tablespoons ground cumin
2 tablespoons dried oregano
1 tablespoon table salt
1.5 teaspoons black pepper
6 tablespoons orange juice
2 tablespoons white vinegar
2 tablespoons olive oil

Mix above in blender and process to a coarse paste, about 10 1 second
pulses.

Rinse pork, pat dry, the rub in paste, being sure to get it in the
slits. Refrigerate like that until ready to grill (I’ve always just
grilled it immediately).

Grilling:
The meat needs to cook to 190. That is about 6 hours on a gas grill on
low. An alternative recommendation was on a charcoal grill until it
fell below 225 degrees, then in the oven at 325 degrees for another 2-3
hours. Alternatively cook for about 6 hours in an oven at 325.

On the grills, heat one side of the grill, put the pork on the other
side, most of the skin away from the heat, and shield the side towards
the heat with aluminum foil for the first half of cooking, then remove
for the second half.

For any method, flip the meat about half way through the cooking.

After cooking the meat, let rest for 1 hour. Then, remove the skin in
one piece and scrape the fat off of the back of it. Also scrape the
fat off the meat. Cut the pork from the bone in 3-4 pieces (I have yet
to be able to remove it so neatly), then slice against the grain into
1/4″ slices.

Drizzle mojo sauce over sliced pork just before serving.

Mojo Sauce:
I bought a bottle of Goya brand. Below is a recipie for it that I
haven’t tried. BTW, the store bought sauce also has lemon juice and no
vinegar in it according to the ingrediants label.

Make up to a day in advance.

4 medium garlic cloves, pressed or minced
2 teaspoons kosher salt
1/2 cup olive oil
1/2 teaspoon ground cumin
1/4 cup distilled white vinegar
1/4 fresh orange juice
1/4 teaspoon dried oregano
1/8 teaspoon ground black pepper.

Using the flat side of a chefs knife on a cutting board, drag the garlic
and salt back and forth in a circular motion until they are ground to a
smooth paste. Heat the olive oil in a medium sauce pan over medium
until shimmering. Add garlic past and cumin and cook, stirring, until
fragrant, about 30 seconds. Remove pan from heat and whisk in
remaining ingrediants. Transfer to bowl and cool to room temperature.
Whisk to recombine before serving.