J-3 Cub pilot reported engine failure during takeoff climb resulting in an immediate turn back and landing.

Narrative

The purpose of today's flight was to pick up my Piper J-3 Cub from it's annual inspection at ZZZ airport. An additional purpose was to fly for at least an hour and perform at least three full-stop landings to reset currency and build proficiency. Furthermore; the Cub was just coming out of the shop for the last three months after ground-damage occurred during a thunderstorm. The aircraft had previously been signed back into service by a very experienced Piper J-3 Cub pilot (who was also Mechanic #2 who performed the tube and skin repairs after the storm damage). I performed the preflight inspection inside the hangar at ZZZ airport while Mechanic #1 secured the new ICS (Intercommunication System) box to the inside of the Cub. I performed a very detailed and thorough inspection; however I did not sump the fuel because I didn't want it to leak on the hangar floor. I called for the fuel truck and told them to hold off for about 15 minutes. When the fuel truck arrived; we pulled the Cub outside but I forgot to strain the fuel. I asked the fueler if I could fuel the airplane myself since the Cub has a high propensity of spilling when topping off. He obliged. I carefully topped on the Cub. The Cub took 7 gallons of the 12 gallon tank; meaning that the tank had been sitting at approximately 5 gallons for 3 months (plus what it burned when Mechanic #2 performed the maintenance test flight several weeks prior).I filed my flight plan. I had previously filed my ADAPT request earlier in the morning. I departed ZZZ without incident. Then I flew to ZZZ1 and performed two full-stop landings with taxi-back for a full-length takeoff. After the second takeoff; I requested a touch-and-go with ZZZ2 Tower. They instructed me to enter a right downwind for Runway XX. On downwind; ZZZ2 Tower cleared me for a touch-and-go and instructed me to make left traffic on the go. I entered a very short base. I verified that carburetor heat was on prior to making my descent. I performed a spot landing on the numbers 15; touching down at around 40 MPH. I then turned off the carburetor heat; applied full power and began to rotate. I climbed out at approximately 60 MPH. At approximately 300 feet AGL; with 5;200 feet of runway remaining; my engine lost all power and my propeller slowed to the point where I could see the wood grain. I pushed the nose forward for 60 MPH; keyed up the microphone with a calm voice and said; 'Engine Failure'. I then heard Tower cancel the landing clearance for the #2 aircraft. At approximately 25 feet AGL; the engine began producing power again. I rounded out the flare touching down higher than normal (approximately 60 MPH). Before I could clear the runway; Tower asked if I needed any assistance. I told them that I believe I could clear the runway. I taxied off at Taxiway J (3;800 feet from the threshold of Runway XX and with 3;200 feet of runway remaining). I taxied to my hangar without incident and thanked Tower for their help. I plan to return to ZZZ1 later today to sump the fuel and check for any contamination. On my drive home; I notified both mechanics of the event and the FBO at ZZZ who had fueled me.