How to bring column value from another data frame in python?

Question

My df1:

df1 = pd.DataFrame({'Col1' : ['A_B_C', 'A_B_C', 'A_B_C', 'D_E_F', 'D_E_F', 'G_H', 'A_B_C'],
                    'Col2' : ['red', 'red', 'red', 'ash', 'ash', 'green', 'red']})

df1

My df2:

df2 = pd.DataFrame({'ID_Number' : [100, 200, 300, 400, 500],
                    'Col1' : ['A_B_C', 'D_E_F','G_H', 'DD', 'WW'],
                    'Col2' : ['red',  'ash', 'green', 'black', 'sky']})

df2

I would like to match the df1 col1 value with the df2 col1 value. If the df1 col1 value exactly matches the df2 col1 value, then bring the corresponding ID_Number from df2.

My Desired Result would be :

ID_Number Col1   Col2
100   A_B_C  red
100   A_B_C  red
100   A_B_C  red
200   D_E_F  ash
200   D_E_F  ash
300   G_H    green
100   A_B_C  red

I tried this way : My_desire_df = df2['Col1'].map(df1.set_index('Col1')['ID_Number']) My_desire_df but no getting the desired result as below

My Desired Result would be :

ID_Number Col1   Col2
100   A_B_C  red
100   A_B_C  red
100   A_B_C  red
200   D_E_F  ash
200   D_E_F  ash
300   G_H    green
100   A_B_C  red