Which physical device accomplish the task of pulse shaping?
It's a combination of two processes: first, you create a discrete-time signal that is pulse-shaped. Then, the DAC converts it to an anlog signal. (And, in a radio, the analog front-end following the DAC converts it to an RF signal).

The discrete-time part is usually done as follows (using Matlab here for convenience). Assume a BPSK data vector data. First, the vector is upsampled to get the desired symbol rate. For example, if the sampling frequency is $f_s = 100$, and the symbol rate is $R_s = 10$, then you must output one symbol every $100/10 = 10$ samples, which means you need to insert 9 zeros between samples:

data_up = upsample(data, 10);


Then, assuming the pulse shape is stored in vector p, the pulse-shaped signal is

data_ps = conv(data_up, p);


Then, data_ps is the input to the DAC, which converts it into a continuous-time pulse-shaped baseband BPSK signal.