how to get a better execution plan for empty sets?
To reproduce your issue, I created three tables with 1000 rows. The view definition does left outer joins on the primary keys of the table which should allow for join elimination. Here's the code:

CREATE TABLE dbo.BASE_TABLE (ID BIGINT NOT NULL, PRIMARY KEY (ID));
INSERT INTO dbo.BASE_TABLE WITH (TABLOCK)
SELECT TOP (1000) ROW_NUMBER() OVER (ORDER BY (SELECT NULL))
FROM master..spt_values;

CREATE TABLE dbo.COL1_TABLE (ID BIGINT NOT NULL, COL1 VARCHAR(1), PRIMARY KEY (ID));
INSERT INTO dbo.COL1_TABLE WITH (TABLOCK)
SELECT TOP (1000) ROW_NUMBER() OVER (ORDER BY (SELECT NULL)), 'A'
FROM master..spt_values;

CREATE TABLE dbo.COL2_TABLE (ID BIGINT NOT NULL, COL2 VARCHAR(1), PRIMARY KEY (ID));
INSERT INTO dbo.COL2_TABLE WITH (TABLOCK)
SELECT TOP (1000) ROW_NUMBER() OVER (ORDER BY (SELECT NULL)), 'A'
FROM master..spt_values;

GO

CREATE VIEW HugeView AS
SELECT b.ID AS B_ID, c1.COL1, c2.COL2
FROM dbo.BASE_TABLE b
LEFT OUTER JOIN dbo.COL1_TABLE c1 ON b.ID = c1.ID
LEFT OUTER JOIN dbo.COL2_TABLE c2 ON b.ID = c2.ID;

GO


The following query access all three tables when it shouldn't have to:

DECLARE @Val BIGINT = 1;
SELECT 1 FROM dbo.HugeView
WHERE (Col1 = 'A' AND @val = 1) OR (Col2 = 'A' AND @Val = 0);


Note the thickness of the arrows in the actual plan:



If I add a RECOMPILE hint then I only get two tables in the actual plan as desired:



Probably the most straightforward fix is to use UNION ALL. Here's the estimated plan:



At first the plan might look bad because it references all three tables. However, the highlighted startup predicate filter is important:



What that means is that branch of the query plan may not be executed depending on the value of the parameter. If I get the actual plan you can see that only one half of the plan was executed:



dbfiddle link for everything in this post.

Note that depending on the complexity of the view the startup filter may not appear in the optimal place. However it should save you some amount of unnecessary work.