Help Powering 2x10W LED using a 15v 1A power supply
If you were to power these correctly you would wire them in series and use a 30V constant current supply such as a Mean Well HLG-40-30B. 

You could use a constant current regulator (like in your link) with a 24-30V DC power supply depending on teh LED's measured forward voltage (Vf).  

CoB LEDs should not be powered in parallel. If they do not go into thermal runaway the current flowing through them will be unbalanced, and likely significantly (20% or more) unbalanced.  





To salvage your setup: 

Measure the voltage (Vf) across the LEDs and calculate the resistor value or try putting a 10Ω 2 watt resistor between the 7812 and LED.

If the LEDs have a Vf of 9V then 300mA will flow.

My guess is now the LEDs are drawing a about 500 mA each and did not burn up because the power supply is maxed out.

It will depend on the actual forward voltage as to how much current will flow with the 10Ω resistors. 

Approximate currents at Vf = 9-12V

 9.0V 300 mA   
10.0V 200 mA  
11.0V 100 mA  
11.9V  10 mA  
12.0V   0 mA


After adding the 10Ω resistors, measure the voltage across the LEDs. 

My guess us they have a Vf of about 9.3V as there are very few 12V CoB LEDs. 

Once you have measured the Vf, use an on line calculator to get the optimal resistor value like this: LED Series Resistor Calculator



Set the current to a level where the LEDs to not get too hot. You should be able to hold your finger on the frame of the LED for a few seconds without major discomfort. 

CoB LED need significant thermal management where the heatsink can cost more than $4.  

Some inexpensive heatsinks that work well with CoBs.
2" round heatsink, $1.39
5.000" Wide, $1.74 per inch  





Not sure why you are using cheap CoBs.  You might get 400 lumens out of them at 300 mA.  When you can buy a very high efficacy (185 lm/W), 280 mm (11") strip of mid power LEDs that can put out over 2000 lumens for under $4:  Bridgelux BXEB-L0280Z-50E1000-C-B3 . These are 19V 700-1400 mA and do not need a heatsink.