I don't know if I've ever seen brunches as such in Spain. I th ink you would have a choice of a hotel with a buffet breakfast (the 12-15 euro type, such as one can find in the Parador) and then ordering cava, as the Spanish don't seem averse to breakfast drinking or, alternatively, waiting unti the mid-day meal.
There is champagne available at the Parador breakfast buffet. Call at 8pm the night before to book a "sitting", advise that you are a pilgrim when you arrive (they may or may not ask to see your Compostela)
15€ and a lovely way to celebrate
We celebrated our wedding anniversary in the Parador in Santiago. There was a superb breakfast buffet on offer in the morning. In the section where there was fresh orange juice, there was also red and white wine and champagne available. We noticed that the gentleman on the table next to us had a glass of wine with his breakfast. We looked at each other and without saying a word, my husband got up and got us 2 glasses of champagne. Such wonderful decadence!!!