Spread your beef bones, and bone marrow on a sheet tray lined with a wire rack. Roast in the oven for 20 minutes or until deeply browned. Spread the tomato paste all over the beef using a brush and pop back in the oven for another 4-5 minutes until it has deepened to a brick red.
Remove the bones from the oven and place into a stockpot and cover with water. Bring to a boil then drop the temperature down to a gentle simmer. After around 30 minutes you’ll see a bunch of foam and fat rise to the top, give it a really good skim and remove as much as you can. After that just skim periodically.
To prep our mirepoix grab one onion and cut it into half inch thick rings. Preheat a pan over high heat and drop the cut onion in. You’re going to blacken the onion rings on one side. This is called an onion Brûlée and it adds a lot of richness and color to your stock. Once one side of the onion is blackened remove from the pan and reserve.
With your remaining onion just cut into equal large pieces along with your celery and carrot. Lightly Dress with oil and roast in the oven at 450f for 10-15 minutes until you have nice color all around. Remove and reserve with your onion brûlée.
After 4 hours of simmering, and occasional skimming, go ahead and add your mirepoix, thyme, bay leaf, and peppercorns. continue to simmer for another 3-4 hours.
Strain your beef stock and use within 5 days or freeze for up to 3 months.
Make the reduction
Warm up two quarts of your homemade beef stock and have it on standby.
Slice your shallots into 1/4″ pieces and smash your garlic.
Preheat a saute pan over medium heat and add a few tablespoons of oil. Add your beef neck and brown all over. Drop in your garlic and briefly toast until it starts to turn golden brown. Add in your shallots and saute, stirring frequently, until the shallots are translucent. Add half of your warm beef stock and bring to a simmer. At this point I like to put my pan slightly off center from the burner so the bubbles push all of the fat to one side making it easier to skim. Have a rubber spatula nearby to clean the sides of your pot. All of that sticky reduced sauce stuck to the side is tasty, try to work it back in before it burns.
After around 30 minutes your sauce should start to thicken up and become viscous, add in the remaining half of beef stock and continue to simmer. You might be like “why reduce it just to thin it out?” well the idea behind this method is to prolong the time the sauce cooks and deepen the flavor. Since there’s a lot more activity going on besides just water evaporating, like Maillard reaction on the side of the pot, sugars caramelizing and so on.
After another 30 minutes your sauce should once again be looking thicker, go ahead and strain it into a smaller pot. This will make the remaining skimmings a lot easier with less stuff in there. Reduce until the sauce is nappe or coats a spoon. Whisk in the cold butter and taste. Adjust your salt and pepper. Reserve warm for serving or cool and use within one week. Freeze for 3 months.