You're not quite there yet. That regulator is a voltage regulator, not a current regulator. LEDs want to be driven with constant current, so you want a constant current regulator (which is exactly what any decent LED driver is). There are some available that are both constant voltage and constant current. These are often described as CVCC or CV-CC supplies.
These are better described as limited voltage, limited current supplies, because they have separate voltage and current limits and which ever one you hit first will engage. For example, say your load is a 1 ohm resistor. That means that for every volt on it, it will conduct 1 amp. Another way to look at it is that for every amp through it, it will have 1 volt across it. Now say you connect it to a CVCC supply set at 1V, 2A. When you connect it, the voltage and current will rise until one of the limits is hit. In this case you will hit 1V before you hit 2A. Thus the supply will regulate at 1V, and the output will be 1A. Now say your resistor changes a bit as it heats up (LEDs do this). Say the resistance changes to 0.9 ohms. The current will rise, but the voltage won't because it can't exceed the 1V setting of the regulator. Say the resistor changes a LOT, down to 0.4 ohms. At 1V, that would mean 2.5A. But the regulator will limit at 2A. Since the resistor will have only 0.8V across it at 2A, the output will have to drop to 0.8V. Now say the resistance continues to drop. The current will stay at 2A, and the voltage will drop.
This is how a CVCC supply works. It can transition smoothly from voltage regulator to current regulator, depending on the load and the settings.
A buck-type or linear regulator will have a voltage limit a little below the input voltage. This differential is sometimes referred to as the dropout voltage. ALL buck-type and linear regulators have this characteristic, though some are not well described. The value of the dropout voltage can range from a small fraction of a volt to several volts. In a regulator with an adjustable output voltage (really a voltage limit), the voltage limit can be adjusted in a range, typically 1.2V at the low end, and input voltage minus dropout voltage at the high end. In some cases the output voltage can be adjusted as low as 0V. Other low-end values are also possible.
Any type of regulator can be built with a current limit. This is not the same as a maximum current. A maximum current is how high you can go before the behavior becomes unpredictable. Exceeding max current can result in any of the following, and more: reg works fine at higher current; reg shuts down; reg reduces output voltage; smoke escapes and nothing ever works again. But when you hit a current limit, the behavior should be very predictable - the output voltage reduces and the current stays at the limit.
Here's an example of a regulator with both constant voltage and constant current adjustments:
http://www.ebay.com/itm/5A-LED-Driv...209?pt=LH_DefaultDomain_0&hash=item5d4b488079
Okay, enough about regulators for the moment. At those power levels, you'll need a heatsink. Anything over 1-2W definitely needs a heatsink. If you're talking 10W per LED, you need substantial heatsink.
You also mention connecting the LEDs in parallel. When you do this, part of the current goes in one LED, and the rest goes in the other. If the LEDs are identical, then the current should split evenly, and if you have a 3A regulator, you'll get about 1.5A in each LED.
If you were to connect them in series, the full output current would go through each LED, but the voltage would be doubled.
