Cromwell and The New Model Armies greatest victory was at Dunbar on September 3 in 1650 against the Scottish armies supporting the young Charles II. After a series of skirmishes and maneuvers between the two armies over the course of a few months, the Scots had trapped Cromwell at Dunbar and cut off his land supply route South to England. I don't have exact numbers of men, but the experienced English army was slightly outnumbered by a raw Scottish force.

The Scots put their main body of cavalry on the right flank, with a smaller group on the left. The Scottish center was full of infantry under 3 commanders. The two commanders of note would be Lumsden on the right flank, and Lawers in the center as shown above. The English matched the Scottish cavalry on the right flank under Lambert, leaving a small amount in reserve under Cromwell. The infantry formed just to the left of Lambert, under Monck. Lastly Dragoons were set at the far left English flank with high ground advantage, and the rest of the Dragoons under Pride were put in reserve with Cromwell.

As for the terrain, a river ran between the 2 armies with the only man made crossing at the Bridge that travels North to Dunbar. 

The battle started in the early morning, still dark, with English cannons starting a barrage of Scottish troops while troops moved to secure the crossing. The Scots returned fire and they had an on and off exchange until daybreak. 

Once light, Lambert and his Cavalry (English) charged against the Scottish cavalry and heavy fighting began. Monck and his infantry (English) marched across the bridge and quickly broke Lumsden's infantry (Scots), forcing Lawers' infantry (Scot) to engage Monck's. As Monck and Lawers fought on, Cromwell ordered Prides Dragoons (English) to support Monck against Lawers. At the same time, Cromwell took his cavalry to join Lambert's (English) attack against the Scottish horse. Together Cromwell and Lambert broke the Scottish cavalry and prepared to charge into the flank of the Scot infantry under Lawers who was engaged with Monck and Pride. Once the cavalry charged, the Scottish were defeated and were completely routed. In Cromwell's honor the Dunbar medal was founded and awarded to him for his service in the battle. This award would not be given again until 1815 after the battle of Waterloo.

Plant, David. “The Battle of Dunbar 1650.” The Battle of Dunbar, 1650, 2011, bcw-project.org/military/third-civil-war/dunbar.