Heat The Olive Oil In A Large Skillet Over Medium-High Heat. Sear The Pork In The Hot Oil Until Browned On All Sides, About 10 Minutes. Place Into A Slow Cooker Along With The Cumin, New Mexico Chiles, Quartered Onion, Garlic, And 1 Minced Jalapeno Pepper. Pour In The Water, Cover, And Cook On High For 6 To 8 Hours, Then Reduce Heat To Low And Cook Until The Pork Is Tender And Easily Shredded, 12 To 16 Hours More. Once Cooked, Remove The Pork And Vegetables To A Large Bowl And Shred Finely With Two Forks. Mix In Enough Cooking Liquid To Moisten The Meat To Your Taste. Prepare The Pico De Gallo 2 To 6 Hours Before The Carnitas Will Be Ready. Combine The Tomatoes, Onion, Tomatillos, And 2 Minced Jalapeno Peppers In A Mixing Bowl. Season With Lime Juice, Salt, And Pepper. Mix Well, And Refrigerate Until Ready To Serve.