The best and fastest carbon sequestration begins with better land stewardship, smaller plots planted more diversely – mimicking the diversity of a forest. Trees grow by root interaction in synergy with fungi, different fungi for fruit trees than nuts. For shallower root systems like vegetables, healthy soil relies on the bacteria and microbes it hosts. Industrial Ag kills those microbes, intentionally poisoning the land under the concept of only allowing one seeded species to propagate. It is designed for ease of harvest, at the loss of diversity and the resilience that diversity brings. (Oh, and poisons usually stay with industrial crops all the way to your table.)
Smaller farms that use best practices to rejuvenate the soil can both revitalize the local rural economy and sequester carbon (3-7GtCO2/yr!!) Such farms avoid costly industrial chemicals, releasing less N2O. Industrial/corporate Ag has been and will be the death of the land, and the people on it. Examples:

• NOT “new Research” this from 2010, and points to earlier papers:
  Synthetic nitrogen destroys soil carbon undermines soil health
  But that’s just a start. Here are more articles to consider sharing:

Food Forests

• Better soil could trap as much planet warming carbon as transport produces
  How to Use Native Fungi to Improve Soil Quality and Bulletproof Your Food Forest Against Disease
• “Soil without biology is geology, according to “bio-prospector” Jeremy Bradley, a member of the group Soil C Quest which is exploring the use of Food Forest Fungi to boost agricultural yield – while sequestering atmospheric carbon dioxide.
• Soil Survival Benefits from a Fungi
• Scientists find that tropical plants – when grown in ways that mimic the multi-tiered, year round patterns of tropical forests – are productive while being heat tolerant and soil rejuvenating. No surprise, Nature is lush because it evolved to mix and handle the variations of environment without need (or want) of human intervention. Indigenous people learned by watching and experimenting over generations how to supplement, not override the natural patterns. Scientists find strong potential of indigenous agriculture

Permaculture

What is needed to repair lands that have been stripped of their natural patterns. Restoring forests on hillsides requires swales to rehydrate the hill, then establishing soil fungi that are the synergistic partners of trees in forming soil vitality… These are part of the skills taught by PERMACULTURE = the large scale permanent horticulture that needs to replace Industrial Ag and its monoculture process.

Because I live in a region being stripped of its forests, I tend to emphasize forests over prairies, but the deep root systems of prairies are the needed and preferred ecology for many regions of the planet. In terms of doing more, doing better – and still knowing how much needs to be done, this is a set of links promoting low density grazing as another way to get more carbon back into the soil.

Prairies

• Converting tilled cropland to grazed pasture can drive substantial SOC accumulation while providing food and economic return for a landowner. Intensive grazing systems, have been tested and used extensively in temperate regions. These practices increase soil carbon content. Benefits of higher soil nutrient status are well documented.
• “The potential of grazing lands to sequester and store soil C should be reconsidered in order to improve assessments in future GHG inventory reports.”
• “Collectively, conservation agriculture supports ecologically healthy, resilient agroecosystems and simultaneously mitigates large quantities of anthropogenic GHG emissions.”
• Debunking the myth that only industrial agriculture can feed world.
• To restore our soils – feed the microbes.
• In India profitable farming with fewer chemicals

General Carbon Sequestration

• As for the industrial scale Carbon Sequestration? The best process I’m aware of creates carbonate rocks that can replace aggregate used in cement, lowering the net carbon release in using cement. It does have concerns, but consider an idea to recycle used cement – Blue Planet
• What prospects are there for industrial scale carbon sequestration… that are energy efficient? Survivable IPCC projections based on science fiction – reality is far worse (YouTube)