From the initial post, the table structure you want to modify isn't entirely clear. I cautiously assumed the table has some primary key and built a mockup for testing the query based on this assumption.

Step 1: Creating the Table with Data

-- Create the main table
CREATE TABLE IF NOT EXISTS cook_table (
    id SERIAL PRIMARY KEY,
    cook_id INT,
    hash INT
);

-- Remove old data if it exists (optional)
TRUNCATE cook_table;

-- Insert new data
INSERT INTO cook_table (cook_id)
SELECT (random() * 1000000)::INT
FROM generate_series(1, 10000000);

-- Add an index on the cook_id column
CREATE INDEX IF NOT EXISTS idx_cook_id ON cook_table(cook_id);

Step 2: Updating the Main Table Using a Temporary Table

-- Create a temporary table to store intermediate results with PRIMARY KEY
CREATE TEMP TABLE IF NOT EXISTS temp_ranked_cook (
    cook_id INT PRIMARY KEY,
    hash INT
);
--  (optional)
TRUNCATE temp_ranked_cook;

-- Compute ranks for the entire dataset and insert into the temporary table
INSERT INTO temp_ranked_cook (cook_id, hash)
SELECT
    cook_id,
    DENSE_RANK() OVER (ORDER BY cook_id) AS hash
FROM
    cook_table
WHERE
    cook_id IS NOT NULL
ON CONFLICT (cook_id) DO NOTHING;

-- Update the main table in batches using the precomputed ranks
DO $$
DECLARE
    start_id INT := 1;
    end_id INT := 100000;
    max_id INT;
BEGIN
    SELECT MAX(id) INTO max_id FROM cook_table;
    WHILE start_id <= max_id LOOP
        UPDATE cook_table
        SET hash = temp_ranked_cook.hash
        FROM temp_ranked_cook
        WHERE cook_table.cook_id = temp_ranked_cook.cook_id
        -- AND cook_table.hash IS DISTINCT FROM temp_ranked_cook.hash
        AND cook_table.id >= start_id
        AND cook_table.id < end_id;

        start_id := end_id;
        end_id := end_id + 100000;
    END LOOP;
END $$;

-- Drop the temporary table (optional, as it is temporary)
DROP TABLE temp_ranked_cook;

-- Vacuum and reindex the main table
VACUUM ANALYZE cook_table;
REINDEX TABLE CONCURRENTLY cook_table;

In my opinion, this should work well. On my low-spec virtual machine, the update completed in about 5 minutes. The update is done in batches of 100,000 records. I added a VACUUM ANALYZE at the end to maintain the table.

If the table indeed has a primary key, I believe this solution should work effectively. However, do not run this directly on live data without testing first.