This is pretty rough. There's a lot of thrashing as I experiment with this. I apologize if I'm missing something fundamental (which I likely am).

PartialAppPlayground.cs

using System;
using System.Collections.Generic;
using System.Data;
using System.Data.SqlClient;

public class PartialAppPlayground
{
	public static void Initialize()
	{
		Func<IDbConnection> createConnection = () => new SqlConnection();

		var queries = new List<Func<IMessage, IHandlerResult>>();
		// Will not compile. Method signature would have to specify IMessage
		// instead of UsersByLastNameQuery, which has data required by the Handle
		// method; could cast inside Handle, but not sure if I want to go down
		// that road
		queries.Add(message => UsersByLastNameQueryHandler.Handle(message, createConnection));

		// Ideally, would like to be have everything registered to the point of being able
		// to call from MVC app as:
		var query = new UsersByLastNameQuery { LastName = "Anderson" };
		var result = someApplicationObject.Handle(query);

		// Would also like to be able to sub dependencies for testing
		Func<IDbConnection> createTestConnection = () => new SqlConnection();
		someApplicationObject.RegisterHandler(message => UsersByLastNameQueryHandler.Handle(message, createTestConnection));
	}
}

public class UsersByLastNameQuery : IMessage
{
	public string LastName { get; set; }
}

public class UsersByLastNameQueryHandler
{
	public static UsersByLastNameQueryResult Handle(UsersByLastNameQuery query, Func<IDbConnection> createConnection)
	{
		using (var connection = createConnection())
		{
			//SQL
			return new UsersByLastNameQueryResult();
		}
	}
}

public class UsersByLastNameQueryResult : IHandlerResult
{
}

public interface IMessage
{
}

public interface IHandlerResult
{
}