What happens to the torque/speed curve of a brushless motor when I increase the voltage?
The torque vs. speed curves presented are the curves for a permanent-magnet, brushed DC motor. The curves are valid for a brushless DC (BLDC) motor to the extent that the BLDC motor controller makes the motor perform like a brushed motor. That is generally the performance provided by many hobby motor-controller combinations. What is missing is an indication of the thermal limits and the control limits.

There is a safe operating torque for continuous operation. That corresponds to the safe operating current for continuous operation. Operation above the safe operating limits for continuous operation is safe for some time. For industrial DC brushed motors, the limit is often 150% of rated current for one minute. For hobby motors, the limits are not consistently published.

The voltages and currents that are often published for BLDC motors are the values for the input to the controller. The controller also likely has a minimum input voltage. That will set the limit of the downward movement of the curve.