import geopandas as gpd

df1 = gpd.read_file(r'/home/bera/Desktop/gistemp/greens.shp')

df2 = gpd.read_file(r'/home/bera/Desktop/gistemp/buildings.shp')

df2['savedindex']= df2.index #Save the index values as a new column

intersecting = df1.sjoin(df2, how='inner')['savedindex'] #Find the polygons that intersect. Keep savedindex as a series

indexCol = ""  # insert index columns name

spatialCount = intersecting.groupby(indexCol).count()