Converting Our Waste Sustainably (COWS) Act of 2023 This bill establishes an alternative manure management program for eligible dairy and livestock producers and provides specified funds to the program for FY2024 through FY2028. The Department of Agriculture (USDA) must establish an alternative manure management program to award producers contracts to support carbon sequestration and greenhouse gas emissions reductions. Producers must implement management measures that include adopting pasture-based management; alternative manure treatment and storage practices; a solid separation system (or installing a new, higher efficiency solid separation system); or scrape technologies, including vacuum technologies. USDA may provide a 100% federal cost share. Further, the bill caps the maximum payment to a person or legal entity in any five-year period at $825,000. USDA must prioritize contracts to entities that address public health concerns (e.g., air quality and water quality) associated with dairy and livestock operations located near low-income or underserved communities. Further, USDA must ensure geographical diversity when awarding contracts. USDA must also use a majority of the program's funds for small and mid-sized dairy and livestock operations, including beginning, limited resource, and socially disadvantaged farmers and ranchers. The bill also includes composting practices as eligible projects under USDA's Environmental Quality Incentives Program and Conservation Stewardship Program. Finally, USDA must review practice standards for composting facilities and soil carbon amendments (e.g., compost) and develop and implement a new conservation practice standard for the on-farm production of compost.